Chapter Five Homework
Connor Hamilton
11/19/2017
Consider a population that has a normal distribution with mean \(\mu = 36\), standard deviation \(\sigma = 8\)
The sampling distribution of \(\bar{X}\) for samples of size 200 will have what distribution, mean, and standard error?
Use
Rto draw a random sample of size \(200\) from this population. Conduct EDA on your sample.Compute the bootstrap distribution for your sample mean, and note the bootstrap mean and standard error.
Compare the bootstrap distribution to the theoretical sampling distribution by creating a table like Table 5.2.
Repeat parts a-d for sample sizes of \(n = 50\) and \(n = 10\). Carefully describe your observations about the effects of sample size on the bootstrap distribution.
Your answers: x <-N(36,8)
Xbar ~ N(36, 8/sqrt(200))
# Your code here
set.seed(13)
sample <- rnorm(200, 36, 8)
hist(sample)
xbar <- mean(sample)
sDxbar <- sd(sample)# Your code here
N <- 10^4
bMean <- numeric(N)
for(i in 1: N) {
bMean[i] <- mean(sample(sample, 200, replace = TRUE))
}
bMeanBar <- mean(bMean)
bMeanBar[1] 35.87956bsError <- sd(bMean)
bsError[1] 0.5815149hist(bMean)
# Your code here
smatrix <- matrix(data = c(30, 8, 36, 8/sqrt(200),xbar, sDxbar, bMeanBar, bsError), ncol = 2, byrow = TRUE)
dimnames(smatrix) <- list(c("pop","sampling","sample","bootstrap"), c("mean", "sd"))
knitr::kable(smatrix)| mean | sd | |
|---|---|---|
| pop | 30.00000 | 8.0000000 |
| sampling | 36.00000 | 0.5656854 |
| sample | 35.87853 | 8.1760899 |
| bootstrap | 35.87956 | 0.5815149 |
Parts a-d for \(n = 10\):
x <- N(36, 8) Xbar ~ N(36, 8/sqrt(10))
# Your code here
sample <- rnorm(10, 36, 8)
hist(sample)
xbar <- mean(sample)
sDxbar <- sd(sample)# Your code here
set.seed(31)
N <- 10^4
bMean <- numeric(N)
for(i in 1: N) {
bMean[i] <- mean(sample(sample, 10, replace = TRUE))
}
bMeanBar <- mean(bMean)
bMeanBar[1] 39.06064bsError <- sd(bMean)
bsError[1] 3.000732hist(bMean)
# Your code here
smatrix <- matrix(data = c(30, 8, 36, 8/sqrt(10),xbar, sDxbar, bMeanBar, bsError), ncol = 2, byrow = TRUE)
dimnames(smatrix) <- list(c("pop","sampling","sample","bootstrap"), c("mean", "sd"))
knitr::kable(smatrix)| mean | sd | |
|---|---|---|
| pop | 30.00000 | 8.000000 |
| sampling | 36.00000 | 2.529822 |
| sample | 39.03270 | 9.960148 |
| bootstrap | 39.06064 | 3.000732 |
Parts a-d for \(n = 50\):
X <- N(36, 8) Xbar ~ N(36, 8/sqrt(50))
# Your code here
set.seed(13)
sample <- rnorm(50, 36, 8)
hist(sample)
xbar <- mean(sample)
sDxbar <- sd(sample)# Your code here
set.seed(31)
N <- 10^4
bMean <- numeric(N)
for(i in 1: N) {
bMean[i] <- mean(sample(sample, 50, replace = TRUE))
}
bMeanBar <- mean(bMean)
bMeanBar[1] 35.79678bsError <- sd(bMean)
bsError[1] 1.092309hist(bMean)
# Your code here
smatrix <- matrix(data = c(30, 8, 36, 8/sqrt(50),xbar, sDxbar, bMeanBar, bsError), ncol = 2, byrow = TRUE)
dimnames(smatrix) <- list(c("pop","sampling","sample","bootstrap"), c("mean", "sd"))
knitr::kable(smatrix)| mean | sd | |
|---|---|---|
| pop | 30.00000 | 8.000000 |
| sampling | 36.00000 | 1.131371 |
| sample | 35.78865 | 7.800473 |
| bootstrap | 35.79678 | 1.092309 |
Your Answer here.
- We investigirlsAte the bootstrap distribution of the median. Create random samples of size \(n\) for various \(n\) and bootstrap the median. Describe the bootstrap distribution. Change the sample sizes to 36 and 37; 200 and 201; 10,000 and 10,001. Note the similarities/dissimilarities, trends and so on. Why does the parity of the sample size matter?
set.seed(31)
even <- 14
odd <- 15
asa <- rnorm(even)
aso <- rnorm(odd)
N <- 10^4
evenBoot <- numeric(N)
oddBoot <- numeric(N)
for (i in 1:N)
{
xEven <- sample(asa, even, replace = TRUE)
xOdd <- sample(aso, odd, replace = TRUE)
evenBoot[i] <- median(xEven)
oddBoot[i] <- median(xOdd)
}
Median <- c(evenBoot, oddBoot)
Parity <- rep(c("n = 14", "n = 15"), each = N)
DF <- data.frame(Median = Median, Parity = Parity)
ggplot(data = DF, aes(x = Median)) +
geom_histogram(fill = "red", color = "blue") +
theme_bw() +
facet_grid(Parity ~.)
Figure 1: Histograms of bootstrapped median values
set.seed(31)
# Your code here
set.seed(31)
even <- 36
odd <- 37
asa <- rnorm(even)
aso <- rnorm(odd)
N <- 10^4
evenBoot <- numeric(N)
oddBoot <- numeric(N)
for (i in 1:N)
{
xEven <- sample(asa, even, replace = TRUE)
xOdd <- sample(aso, odd, replace = TRUE)
evenBoot[i] <- median(xEven)
oddBoot[i] <- median(xOdd)
}
Median <- c(evenBoot, oddBoot)
Parity <- rep(c("n = 14", "n = 15"), each = N)
DF <- data.frame(Median = Median, Parity = Parity)
ggplot(data = DF, aes(x = Median)) +
geom_histogram(fill = "red", color = "blue") +
theme_bw() +
facet_grid(Parity ~.)
Figure 2: Histograms of bootstrapped median values
set.seed(31)
# Your code here
even <- 200
odd <- 201
asa <- rnorm(even)
aso <- rnorm(odd)
N <- 10^4
evenBoot <- numeric(N)
oddBoot <- numeric(N)
for (i in 1:N)
{
xEven <- sample(asa, even, replace = TRUE)
xOdd <- sample(aso, odd, replace = TRUE)
evenBoot[i] <- median(xEven)
oddBoot[i] <- median(xOdd)
}
Median <- c(evenBoot, oddBoot)
Parity <- rep(c("n = 14", "n = 15"), each = N)
DF <- data.frame(Median = Median, Parity = Parity)
ggplot(data = DF, aes(x = Median)) +
geom_histogram(fill = "red", color = "blue") +
theme_bw() +
facet_grid(Parity ~.)
Figure 3: Histograms of bootstrapped median values
set.seed(31)
# Your code here
even <- 10000
odd <- 10001
asa <- rnorm(even)
aso <- rnorm(odd)
N <- 10^4
evenBoot <- numeric(N)
oddBoot <- numeric(N)
for (i in 1:N)
{
xEven <- sample(asa, even, replace = TRUE)
xOdd <- sample(aso, odd, replace = TRUE)
evenBoot[i] <- median(xEven)
oddBoot[i] <- median(xOdd)
}
Median <- c(evenBoot, oddBoot)
Parity <- rep(c("n = 14", "n = 15"), each = N)
DF <- data.frame(Median = Median, Parity = Parity)
ggplot(data = DF, aes(x = Median)) +
geom_histogram(fill = "red", color = "blue") +
theme_bw() +
facet_grid(Parity ~.)
Figure 4: Histograms of bootstrapped median values
Your answer: The parity of medians matter because even produces two you have to look at while the odd only produces one.
Import the data from data set
Bangladesh. In addition to arsenic concentrations for 271 wells, the data set contains cobalt and chlorine concentrations.Conduct EDA on the chlorine concentrations and describe the salient features.
Bootstrap the mean.
Find and interpret the 95% bootstrap percentile confidence interval.
What is the bootstrap estimate of the bias? What fraction of the bootstrap standard error does it represent?
Bangladesh <- read.csv("http://www1.appstate.edu/~arnholta/Data/Bangladesh.csv")
head(Bangladesh) Arsenic Chlorine Cobalt
1 2400 6.2 0.42
2 6 116.0 0.45
3 904 14.8 0.63
4 321 35.9 0.68
5 1280 18.9 0.58
6 151 7.8 0.35The Chlorine variable has some missing values. The following code will remove these entries:
chlorine <- subset(Bangladesh, select = Chlorine, subset = !is.na(Chlorine), drop = TRUE)Your answers:
# Your code here
ggplot(data = data.frame(chlorine), aes(x = chlorine)) +
geom_histogram(fill = "red", binwidth = 50)
mean(chlorine)[1] 78.08401sd(chlorine)[1] 210.0192The mean is 78.08401 and the standard deviation is 210.0192.
# Your code here
N <- 10^4
values <- numeric(N)
for(i in 1: N)
{
values[i] <- mean(sample(chlorine, length(chlorine), replace = TRUE))
}
mean(values)[1] 77.96584The mean of the bootstrap is 77.96584.
# Your code here
confidence <- quantile(values, c(.05, .95))
confidence 5% 95%
58.29251 99.76554 - The bootstrap bias is -0.1256101 which is within 9.146728618^{-5} of the standard error
- Consider Bangladesh chlorine (concentration). Bootstrap the trimmed mean (say, trim the upper and lower 25%) and compare your results with the usual mean (previous exercise).
Your answer:
# Your code here
N <- 10^4
trimMean <- numeric(N)
for(i in 1: N)
{
trimMean[i] <- mean(sample(chlorine, length(chlorine), replace = TRUE), trim = .25)
}
mean(trimMean, trim = .25)[1] 17.64606The values are smaller because the top 25% and bottom 25% are removed from the data. This does make the estimate closer because the outliers are removed
The data set
FishMercurycontains mercury levels (parts per million) for 30 fish caught in lakes in Minnesota.Create a histogram or boxplot of the data. What do you observe?
Bootstrap the mean and record the bootstrap standard error and the 95% bootstrap percentile interval.
Remove the outlier and bootstrap the mean of the remaining data. Record the bootstrap standard error and the 95% bootstrap percentile interval.
What effect did removing the outlier have on the bootstrap distribution, in particular, the standard error?
FishMercury <- read.csv("http://www1.appstate.edu/~arnholta/Data/FishMercury.csv")
head(FishMercury) Mercury
1 1.870
2 0.160
3 0.088
4 0.160
5 0.145
6 0.099Your answers:
# Your code here
x <- ggplot(FishMercury, aes(x=Mercury))
y <- ggplot(FishMercury, aes(x=Mercury,y=Mercury))
graph1 <- x + geom_histogram(aes(y = ..density..), fill = "red")+ geom_density(color = "purple", size = 1.75)
graph1 <- x + geom_histogram(aes(y = ..density..), fill = "red")+ geom_density(color = "purple", size = 1.75)
graph2 <- y + geom_boxplot() + coord_flip()
graph1
graph2
Answer to a the mean is 0.2013456 and the standard deviation is 0.3123153 Note that there is one value (1.87) very far removed from the rest of the values.
# Your code here
simulation = 10^4
bootMean <- numeric(simulation)
mFish <- FishMercury[,1]
for(i in 1:simulation){
bootMean[i] <- mean(sample(mFish,length(mFish),replace=TRUE))
}
Confident <- quantile(bootMean, prob = c(.025, .975))The Boot mean is 0.1527431 the Standard error 0.0575869 and a bias of -1.432435330^{-5}. The confident interval is 0.1078667 and 0.31009
# Your code here
fishN <- FishMercury[FishMercury < max(FishMercury)]
bootMeanN <- numeric(simulation)
for(i in 1:simulation){
bootMeanN[i] <- mean(sample(fishN,length(fishN),replace=TRUE))
}
confidentNew <- quantile(bootMeanN,prob =c(.025,.975))The new mean 0.1167368 the new Standard error 0.083184 the new confidence interval is 0.113 and 0.124594. d.
Removing the outlier changed our information. The mean reduced by 0.0043011%. The standard error decreased by 0.0078499%.
In section 3.3, we performed a permutation test to determine if men and women consumed, on average, different amounts of hot wings.
Bootstrap the difference in means and describe the bootstrap distribution.
Find a 95% bootstrap percentile confidence interval for the difference of means and give a sentence interpreting this interval.
How do the bootstrap and permutation distribution differ?
BeerWings <- read.csv("http://www1.appstate.edu/~arnholta/Data/Beerwings.csv")
head(BeerWings) ID Hotwings Beer Gender
1 1 4 24 F
2 2 5 0 F
3 3 5 12 F
4 4 6 12 F
5 5 7 12 F
6 6 7 12 FfemaleWings <- BeerWings %>%
filter(Gender == "F") %>%
select(Hotwings)
maleWings <- BeerWings %>%
filter(Gender == "M") %>%
select(Hotwings)
mean(maleWings$Hotwings)[1] 14.53333Your answers:
# Your code here
N <- 10^4
maleMeans <- numeric(N)
femaleMeans <- numeric(N)
for(i in 1: N)
{
maleMeans[i] <- mean(sample(maleWings$Hotwings, length(maleWings$Hotwings), replace = TRUE))
femaleMeans[i] <- mean(sample(femaleWings$Hotwings, length(femaleWings$Hotwings), replace = TRUE))
}
meansD <- mean(maleMeans) - mean(femaleMeans)
meansD[1] 5.21402# Your code here
sic <- quantile(maleMeans - femaleMeans, c(.04, .96))
sic 4% 96%
2.666667 7.800000 I am 95% confident that the difference in the amount of wings falls between 2.545455 and 7.4767.
c.They differ by roughly -0.01567 wings.
Import the data from
Girls2004(see Section 1.2).Perform some exploratory data analysis and obtain summary statistics on the weight of baby girls born in Wyoming and Arkansas (do seperate analyses for each state).
Bootstrap the difference in means, plot the distribution, and give the summary statistics. Obtain a 95% bootstrap percentile confidence interval and interpret this interval.
What is the bootstrap estimate of the bias? What fraction of the bootstrap standard error does it represent?
Conduct a permutation test to calculate the difference in mean weights and state your conclusion?
For what population(s), if any does this calculation hold? Explain?
Girls2004 <- read.csv("http://www1.appstate.edu/~arnholta/Data/Girls2004.csv")
head(Girls2004) ID State MothersAge Smoker Weight Gestation
1 1 WY 15-19 No 3085 40
2 2 WY 35-39 No 3515 39
3 3 WY 25-29 No 3775 40
4 4 WY 20-24 No 3265 39
5 5 WY 25-29 No 2970 40
6 6 WY 20-24 No 2850 38Your answers:
# Your code here
# Part a.
girls<-Girls2004
group_by(girls,State) %>%
filter(State =="WY") %>%
summarize(mean(Weight))# A tibble: 1 x 2
State `mean(Weight)`
<fctr> <dbl>
1 WY 3207.9group_by(girls,State) %>%
filter(State =="AK") %>%
summarize(mean(Weight))# A tibble: 1 x 2
State `mean(Weight)`
<fctr> <dbl>
1 AK 3516.35# Your code here
girlsW <- girls %>%
group_by(State) %>%
filter(State=="WY")
girlsA <- girls %>%
group_by(State) %>%
filter(State =="AK")
difference <- mean(girlsA$Weight)- mean(girlsW$Weight)
oSd <- sd(girlsA$Weight) - sd(girlsW$Weight)
simulation <- 10^4
girlsWmeans <- numeric(simulation)
girlsAmeans <- numeric(simulation)
for(i in 1:simulation)
{
girlsWmeans[i] <- mean(sample(girlsW$Weight,length(girlsW$Weight),replace=TRUE))
girlsAmeans[i] <- mean(sample(girlsA$Weight, length(girlsA$Weight), replace = TRUE))
}
difference <- girlsAmeans - girlsWmeans
ggplot(data = data.frame(difference), aes(x = difference)) +
geom_histogram()
boyDifference <- mean(difference)
boyDifference[1] 309.1307boySD <- sd(difference)
boySD[1] 111.8932conf <- quantile(difference,prob=c(.04,.96))
conf 4% 96%
112.445 502.885 I am 95% confident that the weight difference in mean is between 110.235 and 503.237.
# Your code here
bias <- boyDifference - difference
bias [1] 55.0806675 14.8306675 102.6306675 72.0806675 163.9056675
[6] 18.0806675 101.3556675 76.1306675 32.1556675 126.9056675
[11] -59.4193325 -129.5943325 106.2306675 65.6056675 118.0556675
[16] -7.8693325 149.0556675 100.8556675 83.2556675 96.0556675
[21] 35.6806675 -108.1443325 100.7306675 142.1556675 102.0806675
[26] 57.2056675 33.6806675 259.9056675 43.5056675 61.4306675
[31] -250.4443325 137.7556675 108.6306675 -124.2443325 -107.1443325
[36] -37.3193325 8.7056675 103.4556675 3.5806675 -42.4193325
[41] 153.7056675 -108.0943325 356.0806675 116.2306675 -77.2193325
[46] -42.0693325 -69.3443325 21.8556675 68.4306675 -27.6443325
[51] 79.5056675 -98.2193325 40.6306675 -110.9693325 -75.6443325
[56] -1.0443325 9.5556675 -25.8193325 -81.5193325 68.7806675
[61] 24.0056675 142.4556675 -58.6693325 46.0806675 93.3556675
[66] -56.6193325 9.0806675 43.1556675 -17.7943325 48.6556675
[71] -122.1693325 83.4306675 41.2806675 18.9306675 -47.1943325
[76] -69.8193325 -12.9443325 90.8056675 78.1306675 25.8056675
[81] 33.6056675 -123.4193325 -56.6693325 -177.0193325 197.4056675
[86] 21.9056675 -28.6443325 102.0556675 63.4556675 -269.4193325
[91] 186.2556675 1.1556675 70.2306675 -157.7693325 -202.1693325
[96] 34.7056675 -248.1693325 -109.1193325 164.9306675 217.6556675
[101] -115.9943325 8.6056675 -111.9943325 -134.4693325 181.2306675
[106] -11.0193325 -163.9943325 -116.6693325 -63.9693325 -65.8693325
[111] -71.9193325 -16.2193325 -42.8443325 -175.6193325 -71.9443325
[116] 181.6556675 126.0556675 -23.6193325 33.6556675 -167.8943325
[121] -8.9943325 14.1306675 161.5806675 49.0056675 -259.8943325
[126] -55.9943325 0.6056675 -125.3693325 -131.8443325 34.4806675
[131] 157.1806675 -52.1193325 19.4556675 32.7306675 131.3056675
[136] -76.4443325 -173.1693325 51.7056675 -128.0193325 -139.1943325
[141] -97.8193325 -27.4193325 211.2806675 -60.4443325 104.0306675
[146] -64.6443325 21.3306675 98.4806675 141.0306675 69.4556675
[151] -57.8693325 -116.7443325 54.7556675 30.0056675 -62.3443325
[156] -170.1943325 -273.8693325 56.0056675 -158.3693325 -45.9193325
[161] 24.4556675 169.0806675 -39.8693325 31.9556675 -16.6443325
[166] -162.5943325 -30.1693325 -73.5193325 96.0556675 -174.0193325
[171] -139.3443325 -30.9193325 -139.0943325 -83.5443325 28.0306675
[176] 82.6306675 7.6056675 173.8806675 -33.5443325 159.1306675
[181] -122.8693325 -106.4943325 0.9556675 -152.4943325 87.7806675
[186] 23.6306675 158.6056675 55.7306675 -38.5193325 60.4306675
[191] 68.2056675 -82.6443325 -5.4443325 -59.5693325 -49.7693325
[196] -92.9193325 136.3056675 8.4556675 19.2056675 -65.2943325
[201] 87.1056675 142.5556675 109.8056675 63.4806675 -162.3443325
[206] -286.7443325 -157.7193325 -116.4943325 12.1556675 45.6056675
[211] 103.8056675 -138.6693325 31.1306675 70.1306675 108.3306675
[216] -201.8443325 -101.5943325 160.6556675 387.0056675 106.8556675
[221] -98.4443325 18.9806675 -57.6943325 163.2556675 138.7556675
[226] 54.2556675 -95.1693325 -108.5193325 -74.3193325 92.9556675
[231] 10.5556675 170.5556675 178.5806675 100.2306675 -42.1443325
[236] -37.1943325 112.2556675 254.1556675 91.6806675 -212.6943325
[241] -338.0193325 -37.3193325 -59.3943325 35.2056675 -59.5943325
[246] 175.3056675 -103.5443325 35.9306675 -81.1943325 24.0306675
[251] 15.7306675 -156.8443325 74.5806675 50.1556675 75.8806675
[256] -51.0443325 -104.1943325 -79.3443325 -214.1943325 -174.9943325
[261] -69.2443325 -70.6193325 -73.5193325 34.7806675 99.0556675
[266] 26.7556675 -287.3193325 -76.6943325 175.0306675 -34.8443325
[271] -26.8693325 -97.5943325 222.1056675 -99.8943325 86.0306675
[276] 13.9306675 170.5306675 25.1306675 155.4056675 63.8056675
[281] 22.6556675 129.9806675 85.8056675 20.7556675 -241.1193325
[286] -0.8943325 56.7306675 -6.0443325 -16.2943325 -192.5193325
[291] 39.5056675 55.6306675 -178.1193325 76.2806675 -86.2443325
[296] 34.7056675 34.7806675 229.3056675 92.0806675 -135.9693325
[301] 35.1556675 -0.8193325 -30.8943325 -68.6693325 3.7556675
[306] -34.9193325 -10.7693325 23.6556675 -117.8443325 134.1056675
[311] -104.9443325 -15.2443325 -79.1443325 -87.2693325 93.4306675
[316] 40.1806675 -76.8443325 -46.4943325 -156.8193325 -19.3943325
[321] 56.6806675 44.9306675 -189.2943325 13.6806675 61.2806675
[326] 134.1306675 188.5556675 -44.0193325 -108.9193325 89.4056675
[331] 92.0306675 20.3056675 220.1556675 5.0806675 140.2306675
[336] 34.9306675 -37.9693325 -13.8193325 -95.4193325 -8.2193325
[341] -325.0443325 43.6556675 64.5806675 77.5306675 -13.2943325
[346] 68.6306675 -153.9943325 62.1556675 -96.6443325 148.2806675
[351] -16.2443325 103.1306675 -52.3943325 158.1306675 -128.9693325
[356] 100.8806675 -205.9443325 8.6306675 26.0056675 38.9556675
[361] 25.1806675 121.9306675 197.1556675 181.9806675 58.3806675
[366] 27.0806675 -12.5943325 61.2556675 -20.5193325 -72.2943325
[371] -5.4193325 -52.3443325 -221.1443325 57.6806675 -198.3443325
[376] 49.8556675 156.4056675 -28.0193325 -41.2193325 -119.3443325
[381] -32.2943325 -121.6943325 -120.9943325 103.2556675 51.8056675
[386] -75.9693325 56.4556675 92.7306675 77.2806675 -139.0193325
[391] -101.9193325 67.0306675 -29.0693325 -45.2943325 -71.0943325
[396] -135.0193325 85.1556675 -5.1443325 178.4056675 5.2556675
[401] -119.9943325 -85.3693325 10.9806675 -11.6693325 45.8556675
[406] 22.2556675 139.2056675 -247.5943325 -184.5443325 21.8306675
[411] -59.6193325 127.2056675 26.6306675 93.4306675 127.7056675
[416] -119.0443325 -28.1193325 -161.3943325 30.6806675 -27.8943325
[421] -151.9943325 73.4806675 156.0806675 65.6806675 49.4306675
[426] 6.2806675 -7.2443325 -173.8693325 96.5556675 -101.2443325
[431] 180.3556675 1.6056675 77.9306675 67.7306675 -166.0693325
[436] 112.1306675 47.0556675 -106.2193325 -68.8443325 273.8056675
[441] -171.7443325 94.4056675 43.8056675 57.3806675 -249.1943325
[446] 16.2806675 -5.5443325 189.8056675 152.1806675 62.6556675
[451] 155.0056675 -104.3693325 -137.4693325 37.2556675 -42.1193325
[456] -89.0193325 -88.9943325 -34.6443325 117.3556675 61.5556675
[461] -40.1943325 -103.1443325 -150.2943325 -52.7943325 88.0556675
[466] 77.3306675 80.0056675 136.1806675 42.5556675 -11.4943325
[471] 32.4806675 41.8556675 -0.8693325 -148.3943325 -49.0443325
[476] 63.8806675 -249.8693325 -182.6443325 -0.3943325 -118.7943325
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[1676] 46.0306675 90.8306675 -200.9693325 43.4556675 -208.6943325
[1681] -0.1193325 43.8056675 -133.6193325 -123.7443325 54.2806675
[1686] 200.8056675 0.2556675 94.1306675 -2.2193325 9.8056675
[1691] -105.2193325 99.6306675 46.4806675 -52.4443325 282.0806675
[1696] 42.6056675 -1.6943325 172.5306675 -0.0193325 -113.2443325
[1701] 149.6556675 91.9806675 62.3056675 50.4306675 66.3306675
[1706] 97.3306675 198.2556675 152.7806675 -84.8943325 26.6556675
[1711] -98.6943325 87.6056675 6.6806675 -65.1943325 6.9556675
[1716] -122.3193325 12.2056675 95.2306675 -346.5443325 158.0556675
[1721] 226.8306675 34.9806675 -84.6943325 45.7806675 -12.8693325
[1726] 31.0806675 -267.2693325 23.2306675 81.3806675 35.9056675
[1731] -45.2193325 -15.1693325 -187.0443325 54.5056675 -0.6943325
[1736] 85.4306675 -40.2193325 -96.2443325 20.6306675 -107.9443325
[1741] -51.9443325 224.7056675 71.6056675 -44.0943325 63.0556675
[1746] 25.3806675 141.5056675 -219.6693325 27.4056675 -219.0943325
[1751] 66.8556675 -144.4943325 -30.0193325 -24.9943325 -56.6443325
[1756] 83.9056675 -126.6693325 -81.2443325 -223.8693325 104.6056675
[1761] -82.3443325 -15.5943325 121.1556675 118.2306675 -24.1443325
[1766] 73.0306675 -83.9693325 -16.1443325 16.8556675 -95.4193325
[1771] -239.7443325 370.9306675 -127.1193325 167.1056675 -128.2443325
[1776] -106.1193325 -42.4193325 10.1556675 50.1806675 5.4556675
[1781] -126.2443325 52.7556675 140.6806675 68.0806675 58.1306675
[1786] 50.5306675 -30.7443325 -220.7193325 148.8806675 10.6056675
[1791] -5.5943325 -101.5693325 -212.1193325 -313.1443325 -221.5693325
[1796] 241.7306675 57.5056675 47.0306675 -110.7693325 110.6556675
[1801] -33.1943325 -85.9943325 268.2056675 127.3056675 23.1556675
[1806] 13.6806675 -46.9443325 31.9806675 -135.5193325 18.9556675
[1811] 83.5306675 -90.5693325 117.4056675 -62.4943325 -126.0693325
[1816] 23.1056675 -68.3443325 45.1056675 50.8056675 48.4056675
[1821] 143.1806675 -134.4443325 240.1306675 -12.1193325 130.5556675
[1826] 93.0056675 94.1306675 -36.3193325 95.6056675 84.7056675
[1831] 42.9806675 -25.6443325 -81.2193325 -80.6693325 -54.6443325
[1836] 51.6556675 -14.4693325 156.7056675 -21.8193325 0.8056675
[1841] -53.5943325 -26.5943325 161.0806675 -105.2193325 -0.4693325
[1846] 137.3806675 -18.9193325 78.7556675 96.6556675 -113.1443325
[1851] -171.7193325 26.0556675 184.0806675 149.2056675 23.9556675
[1856] 15.4306675 17.7556675 14.1056675 -49.9443325 -8.4193325
[1861] -83.2693325 101.2806675 -137.7693325 -74.4443325 116.4056675
[1866] 61.8806675 -84.6443325 35.7056675 196.0806675 27.8056675
[1871] -27.4443325 52.9306675 139.1806675 -153.0193325 -118.1193325
[1876] 55.6806675 -119.1443325 68.5556675 -79.8943325 -37.5443325
[1881] -151.8443325 -11.8693325 -42.6193325 34.6556675 -54.7943325
[1886] 176.7556675 58.8556675 140.9806675 -4.3193325 -211.6443325
[1891] 0.7056675 -194.4193325 125.1306675 31.6056675 104.8556675
[1896] -57.2193325 -23.5193325 29.5556675 -119.7193325 -23.9443325
[1901] -14.3443325 80.5556675 -156.0693325 -87.6693325 -147.8443325
[1906] -65.9443325 -141.1193325 12.5306675 -209.6193325 -142.8193325
[1911] -105.2443325 42.7306675 143.3556675 186.2806675 137.0556675
[1916] -118.8943325 131.8556675 -109.7193325 11.9556675 -38.2693325
[1921] -56.5193325 -133.2443325 99.9806675 182.7056675 -59.6443325
[1926] 43.7056675 -2.6193325 -110.3693325 -98.9193325 -258.3693325
[1931] 77.3806675 -53.3943325 -184.5943325 169.2056675 -58.0193325
[1936] -87.8443325 -53.5193325 58.9306675 151.6306675 227.8556675
[1941] -130.0443325 75.3556675 63.1806675 -41.8193325 -121.8943325
[1946] 43.5306675 6.3306675 -66.3443325 32.3306675 -112.3193325
[1951] 2.6806675 -50.4443325 182.1056675 62.1306675 -288.5693325
[1956] -62.2943325 276.0056675 -159.9193325 25.7306675 -223.2443325
[1961] -27.5693325 -309.7943325 -29.8693325 136.7806675 -10.6693325
[1966] -291.7693325 78.8806675 -80.7693325 -28.0943325 -105.8693325
[1971] 2.4806675 -50.9943325 76.7306675 -89.9693325 -45.2193325
[1976] -51.4693325 -126.5943325 -52.7693325 190.9056675 33.6306675
[1981] 57.4556675 -14.3443325 -65.6193325 93.1056675 127.7806675
[1986] -33.8443325 -85.3193325 -9.7943325 -15.4193325 -60.2943325
[1991] -119.2943325 151.9306675 -10.1193325 -88.0443325 -119.0443325
[1996] 69.6056675 -150.2693325 -107.8693325 -30.7693325 -153.9443325
[2001] -1.8693325 -28.1693325 -166.1443325 132.0056675 -183.0693325
[2006] 167.7306675 -115.4693325 67.5556675 -100.0693325 73.9806675
[2011] -229.1693325 -168.9693325 -116.6193325 154.8056675 -143.8943325
[2016] 92.0806675 -280.4693325 -153.7693325 301.8306675 -72.4943325
[2021] -58.9443325 -170.9693325 -1.3193325 128.1556675 -23.3693325
[2026] -70.9943325 254.3306675 115.4056675 124.2056675 -0.6693325
[2031] -110.2193325 -16.5443325 -24.1693325 5.3556675 3.6056675
[2036] 80.0056675 157.5806675 65.4306675 16.4806675 -72.3193325
[2041] -11.1943325 -38.7443325 38.7056675 -10.6443325 -4.5443325
[2046] -86.4693325 -44.4943325 115.4056675 41.0056675 -33.7443325
[2051] 93.7556675 -16.4693325 -115.8943325 -108.0943325 218.3806675
[2056] -21.1693325 -14.2193325 177.8556675 -16.8193325 145.7056675
[2061] -127.3193325 -106.8943325 71.1806675 100.1056675 66.1056675
[2066] -125.1693325 123.5306675 266.2806675 -131.0943325 -112.4943325
[2071] -150.7693325 22.2556675 -23.0193325 -101.2193325 84.8306675
[2076] -204.0193325 20.8556675 116.7056675 -36.7693325 -20.8693325
[2081] -257.8443325 -53.2943325 90.6056675 -66.3443325 36.8556675
[2086] -129.3943325 219.0556675 116.5056675 12.0056675 -13.5693325
[2091] -35.0943325 21.5306675 -38.3193325 157.8556675 -142.8443325
[2096] -8.9193325 103.1306675 96.7556675 -108.9193325 -145.3693325
[2101] -38.8693325 85.5306675 -13.1443325 -113.8443325 29.4806675
[2106] 151.0556675 -22.8693325 15.8556675 76.7306675 -5.3943325
[2111] 94.8056675 -115.1443325 11.7806675 -166.9193325 -150.4693325
[2116] -39.9443325 -162.5193325 -80.6693325 -1.6693325 3.5556675
[2121] 11.3806675 -146.4943325 99.6056675 125.2556675 -251.3443325
[2126] 180.5306675 16.4806675 -98.4443325 86.6806675 -12.2193325
[2131] 28.6806675 -2.1693325 136.8806675 -183.1693325 48.8306675
[2136] 115.9806675 -57.7693325 -166.5943325 -171.0443325 54.9306675
[2141] -148.3193325 25.2056675 57.5806675 -15.2693325 -91.5693325
[2146] -47.2693325 61.9056675 57.2056675 -63.4943325 -22.3443325
[2151] -47.0943325 48.5056675 73.6556675 113.6056675 -187.3193325
[2156] 89.9056675 206.6306675 -70.1193325 -18.1693325 -90.5443325
[2161] 107.2056675 37.2056675 -130.1693325 7.9556675 129.4806675
[2166] 1.1306675 -44.9193325 -15.7693325 85.5306675 36.5556675
[2171] -207.3443325 -211.3693325 -125.0943325 -161.6943325 -188.7193325
[2176] 99.7306675 10.4056675 69.9306675 113.6556675 6.0556675
[2181] -265.6693325 -71.7193325 67.0806675 55.2056675 27.5806675
[2186] 172.4306675 -76.7443325 -48.6193325 123.6056675 -70.3693325
[2191] -136.1693325 -74.8443325 65.4056675 62.9056675 26.8806675
[2196] 104.5556675 -95.6693325 -13.6193325 65.9306675 2.1056675
[2201] 156.1806675 81.9556675 -15.0193325 -100.8693325 -68.6443325
[2206] -48.8943325 67.6556675 -47.6193325 90.8556675 -136.3943325
[2211] -113.9443325 74.7806675 73.8556675 -8.4693325 -131.3443325
[2216] -89.0693325 145.1556675 85.0556675 -58.2443325 -103.6943325
[2221] 207.7806675 11.5306675 33.0556675 -155.4193325 -84.6693325
[2226] 4.8306675 10.5556675 -69.9693325 29.6056675 -126.3693325
[2231] -105.2193325 4.2806675 208.4306675 -32.8693325 269.2556675
[2236] 102.5556675 208.2556675 -76.9693325 -51.7693325 111.0306675
[2241] -30.1943325 -5.2193325 44.8556675 64.8806675 152.4056675
[2246] 96.4306675 13.8556675 251.2056675 94.1806675 100.7306675
[2251] -16.7693325 154.9306675 4.8556675 -13.4943325 42.8556675
[2256] -11.9443325 77.6806675 -33.8443325 4.3806675 -36.8193325
[2261] -50.1443325 -0.6443325 77.4056675 -61.0443325 73.0056675
[2266] -90.8943325 -50.1943325 97.7056675 86.3306675 93.7556675
[2271] 61.5306675 180.7056675 -199.0693325 63.9056675 -66.7943325
[2276] -23.8693325 120.4556675 154.6306675 -53.3693325 -34.0693325
[2281] -200.4443325 58.3556675 -68.0693325 14.5306675 2.2556675
[2286] 91.1556675 11.8056675 -83.9193325 -231.2443325 -58.8193325
[2291] -209.2443325 230.7306675 -3.3693325 -196.0943325 153.1556675
[2296] -85.2693325 128.1806675 29.5056675 -64.2193325 40.1556675
[2301] 4.1806675 161.5556675 -176.1943325 -63.6443325 13.9806675
[2306] 138.2556675 224.8556675 -2.7443325 93.6306675 -174.7443325
[2311] 117.6556675 -3.0693325 159.4806675 -15.4943325 -11.6193325
[2316] -170.1443325 99.2806675 34.7556675 -85.7443325 21.7806675
[2321] -50.8943325 -90.2693325 -96.4693325 -163.7693325 183.2556675
[2326] 29.4056675 185.0556675 91.6556675 18.3806675 7.7056675
[2331] 69.6806675 233.0306675 -73.9443325 -52.6443325 -57.3693325
[2336] -46.8693325 -21.7443325 225.4806675 64.0306675 129.2556675
[2341] -13.1443325 131.1806675 -204.6943325 -122.6943325 -87.7443325
[2346] 205.3306675 -83.6193325 57.8806675 -149.5193325 -84.9693325
[2351] -0.5193325 -148.9443325 -85.7443325 -227.1943325 -78.1193325
[2356] 157.9806675 37.4556675 -105.4693325 -123.7193325 -47.0693325
[2361] 6.6056675 -62.0193325 52.5306675 -65.2193325 -66.7193325
[2366] 260.0806675 -246.6193325 -184.5443325 14.5806675 -13.3443325
[2371] -91.4943325 -328.4443325 -86.7693325 -114.1693325 -78.2693325
[2376] 195.1806675 -115.4943325 51.4056675 -117.3693325 -163.9943325
[2381] -168.9443325 127.6806675 11.4556675 -11.5693325 5.7056675
[2386] -24.4443325 -120.6193325 -73.6943325 148.4806675 -101.0193325
[2391] -117.8443325 126.8806675 -144.7943325 48.6306675 79.2306675
[2396] -92.4943325 -194.7193325 97.2556675 244.9306675 2.9556675
[2401] -201.1193325 12.9806675 75.1056675 17.5056675 153.5306675
[2406] 100.3556675 -137.7693325 -6.0943325 -38.7943325 19.7556675
[2411] 5.5306675 142.0056675 -146.5693325 81.9306675 -154.2443325
[2416] -72.4943325 -100.9693325 -69.1943325 27.3556675 116.0306675
[2421] -65.8693325 36.2806675 -70.8193325 30.0556675 -58.2193325
[2426] 63.5056675 -33.2193325 -204.1193325 -153.0443325 -164.5943325
[2431] 76.7806675 39.8056675 91.5806675 -76.0693325 170.2806675
[2436] -31.7693325 -175.3443325 -110.4443325 -0.1443325 30.6806675
[2441] 126.0306675 -71.8693325 -72.1193325 187.7056675 -83.3943325
[2446] 172.0306675 -136.5443325 124.3306675 54.2556675 30.9306675
[2451] 98.5556675 128.5556675 -0.0943325 -205.6193325 7.6306675
[2456] 133.5306675 14.8306675 -143.9193325 67.0806675 158.6806675
[2461] 134.3806675 -157.7693325 -59.5943325 -31.6443325 -34.1443325
[2466] 95.7556675 -21.0693325 38.0306675 68.0306675 -78.5943325
[2471] 71.0806675 -113.8693325 -215.6443325 49.0556675 68.0306675
[2476] 90.8806675 -299.7443325 -192.3693325 -24.0943325 23.3056675
[2481] -43.7443325 34.4306675 123.1056675 -185.9943325 -8.2943325
[2486] -162.5193325 203.3806675 113.4056675 -129.4443325 -11.6693325
[2491] 20.8806675 -106.0943325 18.6806675 72.6806675 39.2056675
[2496] -135.4943325 -20.4693325 40.8056675 -182.5943325 36.8056675
[2501] 66.4056675 -118.1443325 -84.6443325 -170.3693325 17.3056675
[2506] -43.7193325 146.6056675 37.9306675 -46.4943325 -80.2193325
[2511] -112.5693325 121.5806675 174.4556675 -133.7943325 31.3556675
[2516] -65.3943325 -191.4693325 -90.7943325 192.8806675 31.5556675
[2521] -38.0943325 25.2306675 -140.5943325 -118.4693325 -12.2193325
[2526] 194.0306675 -151.2943325 -221.7443325 -10.7943325 -6.6443325
[2531] -37.8693325 -144.1693325 -20.3443325 72.1556675 93.7306675
[2536] 137.8306675 40.9056675 55.0306675 -71.1693325 -17.7193325
[2541] -24.2943325 -105.6193325 48.4056675 -70.9943325 -124.2193325
[2546] -203.9443325 100.8306675 219.4306675 -61.2693325 7.4556675
[2551] 291.6056675 114.6556675 118.1306675 12.1056675 -98.5693325
[2556] 63.4556675 -123.3443325 31.5306675 61.4806675 198.5306675
[2561] 74.8056675 11.0806675 -197.8943325 15.2806675 -93.7443325
[2566] 68.2306675 -99.4443325 -113.7693325 -65.1443325 -122.2193325
[2571] 110.1806675 -73.2693325 221.0056675 -6.7943325 -223.6943325
[2576] 112.6556675 -67.3443325 17.3306675 100.5306675 -58.2443325
[2581] 13.0056675 91.5806675 -96.9443325 -123.0943325 59.6556675
[2586] 95.6806675 -96.3693325 -111.7443325 -63.4443325 113.8306675
[2591] 138.1306675 -78.4693325 -119.5693325 -89.7443325 -118.3943325
[2596] 18.6056675 -116.4943325 -23.3193325 -25.2193325 7.7806675
[2601] -7.1693325 19.4556675 -13.1193325 -104.4943325 49.6556675
[2606] -13.0693325 -145.2943325 -123.1443325 18.7056675 -21.3693325
[2611] 241.1806675 -36.5443325 -39.9443325 44.3306675 82.4556675
[2616] -145.4443325 40.3806675 48.4556675 106.4806675 198.0306675
[2621] -3.6193325 75.8306675 58.6306675 -40.8443325 -189.7943325
[2626] 219.8306675 188.0556675 116.0056675 -174.6693325 -72.4443325
[2631] 7.2056675 -54.3693325 63.0056675 21.5306675 -114.2943325
[2636] -55.2693325 77.7306675 295.1306675 29.5806675 101.2306675
[2641] -44.9193325 -127.1943325 16.4806675 -94.4943325 -203.3443325
[2646] -156.3443325 86.0306675 -112.1193325 42.6056675 129.0056675
[2651] -118.8943325 182.5056675 -15.1443325 52.5556675 113.7056675
[2656] 37.5806675 -44.9943325 -91.3193325 5.6806675 165.0556675
[2661] 11.8556675 -226.6443325 -71.7943325 -55.6943325 160.3306675
[2666] -103.3943325 49.3806675 94.6556675 -146.7943325 -194.3193325
[2671] -270.6693325 16.0806675 -176.4193325 0.3056675 36.2306675
[2676] 242.5056675 -101.3943325 66.9056675 -103.5693325 56.3556675
[2681] 119.8806675 -219.7443325 43.8556675 68.1806675 126.3556675
[2686] 88.2806675 179.6056675 -248.1693325 144.9806675 202.5306675
[2691] 37.7056675 38.1806675 -104.8193325 -20.7943325 132.4056675
[2696] 55.1306675 96.9306675 -8.6443325 71.1556675 -45.4943325
[2701] -44.5443325 245.4556675 -201.0193325 -54.0693325 136.7306675
[2706] 97.7306675 203.4056675 -231.3443325 -118.5193325 34.3056675
[2711] 49.6556675 -51.0943325 -21.7193325 77.8806675 -192.7693325
[2716] 272.5306675 -5.2193325 -35.7443325 -242.5193325 7.9056675
[2721] -20.4193325 -80.3443325 70.3806675 -95.9193325 -4.9943325
[2726] 16.3806675 4.8806675 -220.9193325 -85.2443325 -23.7943325
[2731] -91.6443325 -34.8943325 152.1306675 219.9556675 -105.5443325
[2736] -28.3443325 -42.4443325 105.1806675 29.5556675 -80.7443325
[2741] 133.5806675 -123.6193325 50.9056675 145.7556675 16.3306675
[2746] 157.3556675 -157.3693325 -5.8193325 -6.7943325 -71.8193325
[2751] -102.2193325 6.2306675 -57.1443325 -56.8443325 108.9556675
[2756] 164.3556675 92.8056675 34.1806675 70.5306675 80.1306675
[2761] 79.5806675 -99.3693325 11.7056675 -80.5943325 -22.3693325
[2766] 108.9306675 100.0806675 170.0306675 130.7056675 -118.9443325
[2771] 28.7556675 18.6306675 126.0056675 151.7556675 133.5556675
[2776] -80.2693325 -197.0693325 130.3306675 241.6806675 -85.5193325
[2781] -187.3443325 10.5806675 54.1306675 140.1556675 -105.2193325
[2786] -73.8693325 -87.5443325 -44.2443325 265.9806675 -30.5693325
[2791] -178.8693325 -10.5443325 48.0056675 101.2056675 -38.4693325
[2796] 38.2806675 36.5056675 -36.4943325 -13.1693325 -99.8443325
[2801] -82.9443325 191.3056675 3.9306675 -101.6193325 129.8806675
[2806] -8.4693325 -21.6943325 -59.8193325 -184.5693325 -126.1693325
[2811] 52.3556675 97.3556675 73.9306675 26.1306675 95.5306675
[2816] 124.8306675 -83.0193325 180.6806675 -21.6943325 -20.6693325
[2821] 94.4806675 -184.9193325 -226.2693325 -21.3693325 -167.1193325
[2826] 59.8806675 -65.3943325 88.3056675 -70.1443325 -68.7193325
[2831] 189.5306675 -23.6943325 22.0806675 261.7056675 55.1056675
[2836] 133.8806675 -157.7443325 -139.2693325 171.3556675 -42.6193325
[2841] -40.7693325 -24.1443325 -43.3193325 187.2056675 78.9056675
[2846] 97.3556675 233.0556675 67.8556675 -10.1443325 -23.2193325
[2851] -58.2943325 104.5056675 36.2556675 -66.7443325 -120.8693325
[2856] -68.8943325 33.2056675 -6.1693325 78.5806675 48.9306675
[2861] -238.7693325 -20.8443325 -158.2943325 76.4056675 -59.3443325
[2866] -11.4693325 -105.7943325 25.6306675 -18.6193325 27.1306675
[2871] 47.8306675 41.4806675 -111.2943325 2.9306675 22.6556675
[2876] 101.4806675 18.2806675 103.3306675 -83.5943325 33.7056675
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[8846] 32.7556675 167.8806675 -176.3693325 95.3306675 -139.3943325
[8851] 223.9056675 70.7806675 -159.4943325 30.6556675 26.0056675
[8856] -118.4193325 14.6556675 44.4306675 -53.2193325 55.9056675
[8861] 16.2806675 106.6056675 102.3556675 34.6306675 -132.6193325
[8866] -28.4693325 155.9556675 -3.3943325 -185.7443325 33.5306675
[8871] 103.8056675 -63.9693325 -25.7943325 -119.7943325 -57.5943325
[8876] 184.3056675 -22.2443325 21.7306675 44.0556675 191.0556675
[8881] -51.5943325 268.6056675 -144.2193325 -151.7943325 166.1556675
[8886] -189.3693325 5.4056675 -0.8693325 66.9806675 74.7306675
[8891] 118.0556675 104.1806675 80.0306675 111.9556675 -6.4693325
[8896] -23.1193325 -69.2943325 111.4306675 -49.3193325 45.7806675
[8901] -152.3193325 71.0556675 -32.3443325 -64.5943325 -37.1193325
[8906] -232.3943325 142.1306675 -31.5693325 155.6306675 25.9556675
[8911] -91.3943325 -142.8693325 -67.2193325 -27.7943325 -82.2943325
[8916] -115.5693325 -67.2193325 -48.7193325 43.1056675 -49.1693325
[8921] 206.1806675 -98.3693325 151.9056675 94.5556675 -96.1193325
[8926] 80.7556675 73.1056675 -93.7193325 -11.3693325 147.4306675
[8931] -162.9693325 94.0556675 56.2556675 122.7806675 124.2806675
[8936] 37.1806675 11.7556675 229.2556675 -24.3443325 163.1556675
[8941] 5.2556675 -30.7693325 -289.5943325 -431.3193325 223.3306675
[8946] -1.1443325 125.4306675 -95.6443325 -45.2193325 -124.4443325
[8951] -30.8443325 -70.8693325 71.1806675 -22.7443325 112.5806675
[8956] -95.8693325 1.5056675 -19.6193325 -193.7443325 -140.6693325
[8961] -97.5193325 158.9306675 -46.4193325 -155.3693325 -123.0693325
[8966] 1.8806675 16.6306675 184.4556675 4.6806675 -140.2943325
[8971] -3.7693325 75.0556675 20.4056675 71.2306675 -84.2193325
[8976] -141.4193325 -41.9943325 105.6556675 -223.2193325 -199.1193325
[8981] 127.6306675 118.3806675 -26.3943325 -149.6943325 158.5306675
[8986] -15.7943325 -21.4193325 183.8056675 -120.3943325 125.9556675
[8991] -200.7443325 -1.5193325 -23.7443325 -72.0693325 123.1056675
[8996] -81.1443325 -124.3443325 196.3556675 -46.6943325 20.9556675
[9001] 138.9056675 -155.1943325 166.1056675 71.3806675 52.9056675
[9006] 62.0556675 144.0806675 104.5306675 -49.8693325 183.1806675
[9011] -5.1443325 -139.9943325 24.0306675 59.4806675 20.3806675
[9016] -16.3443325 -179.1193325 45.9306675 132.4306675 -147.5443325
[9021] -259.8193325 -33.8193325 -58.8193325 -61.5443325 -192.6693325
[9026] -121.0193325 18.2556675 -59.2443325 256.5056675 160.9806675
[9031] 64.8306675 -61.2693325 31.2806675 -152.6443325 40.1806675
[9036] 31.3306675 79.0556675 100.5056675 -144.5443325 132.4306675
[9041] 102.6056675 -106.7943325 -160.2943325 101.1806675 9.6806675
[9046] -161.6443325 54.0556675 63.0306675 30.3806675 -16.6693325
[9051] 116.0556675 -243.4443325 47.0056675 -188.9943325 95.7056675
[9056] 162.3306675 -91.5193325 -141.2943325 -93.1193325 -141.3443325
[9061] 39.9806675 67.5556675 14.2806675 -37.4443325 -35.8943325
[9066] 5.6806675 93.9056675 -98.0193325 -66.3193325 -158.3443325
[9071] 25.2556675 305.8306675 -44.7943325 35.8306675 -80.8443325
[9076] -170.4193325 -239.0693325 69.9056675 93.5556675 39.5056675
[9081] 52.9306675 -148.7693325 -34.4193325 76.4556675 -19.0193325
[9086] 88.4806675 -12.9693325 85.5556675 -143.5943325 -0.7943325
[9091] 18.0556675 -38.7943325 -65.3443325 175.9056675 158.2806675
[9096] -25.0443325 -48.5943325 -21.9443325 -136.7443325 85.6556675
[9101] -47.2193325 69.7806675 -48.4193325 -86.1943325 -48.3943325
[9106] 188.4306675 -23.0943325 -22.2693325 94.6056675 -127.9443325
[9111] 127.8056675 6.1556675 -229.9693325 -30.1443325 -20.7943325
[9116] 107.3806675 -161.3193325 214.6556675 -81.6443325 -46.4943325
[9121] -42.1943325 158.3306675 -149.8943325 -78.7943325 -26.3943325
[9126] -116.7193325 97.3556675 44.1056675 -46.5193325 -115.6193325
[9131] -8.0943325 71.8306675 -265.7693325 93.8056675 122.7556675
[9136] 29.3306675 142.1306675 -3.6693325 -45.3443325 57.5806675
[9141] -86.1693325 224.6306675 -0.2193325 -93.6443325 -115.8693325
[9146] -6.2443325 73.0306675 -140.2693325 -120.7193325 -42.2693325
[9151] 122.3306675 34.5306675 -13.6193325 -43.2943325 97.6306675
[9156] -128.0943325 -156.5693325 -61.8943325 204.5306675 -32.0193325
[9161] 78.2306675 -202.2193325 -48.5443325 -9.3693325 -144.0943325
[9166] -164.8193325 87.8556675 -73.1443325 -43.6193325 -110.3943325
[9171] 12.1556675 45.2806675 -124.1693325 -55.3693325 68.6806675
[9176] 159.2056675 -17.8193325 138.3306675 5.5806675 6.1556675
[9181] 244.8806675 45.5556675 133.5306675 -29.0693325 11.5056675
[9186] -32.9943325 -199.9943325 -134.2193325 -83.0693325 11.7556675
[9191] -100.2443325 253.3056675 13.1056675 -121.6943325 31.9556675
[9196] -59.0193325 86.1306675 172.7806675 -54.0193325 43.4556675
[9201] 141.3306675 33.3806675 108.3806675 -84.4693325 105.4306675
[9206] -60.3193325 134.6556675 -105.9193325 4.3306675 9.8056675
[9211] -0.3943325 168.3556675 -105.6193325 16.5306675 186.0556675
[9216] 46.1556675 7.5556675 -13.2443325 111.1306675 -77.7693325
[9221] 66.1556675 36.7806675 -122.7443325 5.8306675 159.1056675
[9226] 47.1556675 50.2056675 -42.1943325 77.1306675 -3.8193325
[9231] -28.7943325 107.5806675 134.3556675 117.1056675 -116.6443325
[9236] -1.7693325 -32.3693325 -114.0693325 -35.7693325 -66.9693325
[9241] 42.8306675 44.3806675 225.3056675 31.7306675 -104.6443325
[9246] -93.9693325 -51.4193325 111.7806675 50.3556675 176.5306675
[9251] 6.4556675 113.9306675 82.1806675 96.8056675 -23.0193325
[9256] 52.1806675 -14.0443325 169.1556675 117.3306675 -12.6693325
[9261] -5.9443325 63.8056675 103.8306675 105.1306675 -118.2693325
[9266] -71.4193325 20.3556675 110.0556675 0.9556675 104.0306675
[9271] -60.5443325 -252.3443325 -115.8193325 -100.9193325 17.0306675
[9276] -44.6193325 -9.4443325 62.1806675 -151.6943325 181.7306675
[9281] 35.6556675 -45.1443325 -89.1943325 13.2806675 -185.7193325
[9286] 226.8806675 -68.8193325 -34.6443325 -81.1443325 15.8556675
[9291] 257.2806675 37.9306675 40.1556675 -187.7943325 12.9056675
[9296] -36.6693325 -175.1943325 -140.4443325 13.9556675 108.8306675
[9301] 278.9056675 54.0556675 -34.2193325 -28.7193325 75.7556675
[9306] 254.5306675 22.0806675 -60.7193325 -22.1943325 -59.0193325
[9311] -29.1193325 -97.2693325 14.5556675 -93.0693325 -108.1193325
[9316] -43.9193325 -152.8943325 71.2556675 49.5306675 -131.4943325
[9321] 66.4556675 -45.3943325 -46.9443325 -2.4193325 78.7806675
[9326] 14.2056675 4.6306675 67.1806675 -88.1943325 -151.4193325
[9331] 52.1556675 56.8306675 66.6806675 -90.0193325 -118.9693325
[9336] 153.8806675 -116.9193325 5.5306675 -10.7443325 -7.6193325
[9341] 24.5306675 200.5806675 150.1056675 -128.7943325 5.3056675
[9346] -99.7693325 187.5056675 29.0306675 113.7306675 -85.4693325
[9351] -82.2943325 232.1556675 55.6806675 -28.3693325 225.6556675
[9356] 175.7556675 -109.6943325 191.0556675 -75.5193325 49.2306675
[9361] 155.8056675 51.6306675 45.1556675 -214.7443325 -28.3693325
[9366] 75.9056675 -22.2943325 -86.3943325 -58.9193325 -83.5443325
[9371] -85.7943325 43.5806675 79.6806675 -2.5943325 -14.8693325
[9376] 39.6306675 -177.1193325 157.5056675 -67.2193325 53.6556675
[9381] -42.2693325 -309.5693325 -17.8443325 86.4306675 -55.5193325
[9386] 188.2556675 92.5056675 -55.9193325 -65.5943325 81.2556675
[9391] -4.7693325 -75.9693325 -129.5193325 -263.9443325 -114.0193325
[9396] -143.6693325 97.9806675 -39.7693325 -186.6943325 189.2806675
[9401] -121.0693325 23.5556675 -156.7943325 -171.3193325 41.2056675
[9406] 155.8806675 37.0306675 37.0556675 -121.9943325 -8.2943325
[9411] 135.4056675 210.6306675 -99.4443325 -27.2693325 141.5056675
[9416] 283.1556675 -168.7443325 215.2056675 -30.0693325 92.0306675
[9421] 15.0806675 -279.0193325 15.3806675 94.0806675 -99.2693325
[9426] -104.3693325 12.5556675 21.9306675 126.7556675 -42.1943325
[9431] 139.8306675 123.1556675 84.5806675 94.1806675 -66.4193325
[9436] 143.5806675 92.2056675 -107.6693325 44.1056675 -176.9193325
[9441] 38.4556675 -30.2193325 142.3056675 65.5306675 -13.9943325
[9446] -69.0693325 -7.5943325 38.6306675 -92.3193325 -185.1693325
[9451] 24.5306675 -368.6443325 159.9056675 30.9806675 34.1806675
[9456] -192.7693325 -114.9193325 131.6556675 15.7306675 -6.4193325
[9461] -127.0943325 -158.1443325 -108.6443325 -159.2443325 -11.4693325
[9466] -194.1443325 -124.5193325 48.2556675 62.5806675 -55.7693325
[9471] 191.8056675 3.9306675 164.0306675 -85.1443325 48.6056675
[9476] 28.6806675 -111.2693325 -49.6193325 74.0806675 -66.9943325
[9481] 3.3556675 -6.8193325 -128.4693325 255.4806675 -18.3693325
[9486] 125.9556675 21.5306675 -106.6443325 -77.1693325 52.3056675
[9491] -29.2693325 -119.5943325 -116.2443325 -24.9443325 -43.4443325
[9496] -192.2193325 -105.4443325 45.0556675 27.1806675 -69.5693325
[9501] 59.4056675 3.9556675 55.1306675 68.0306675 9.0306675
[9506] -3.4943325 61.6306675 -135.4693325 2.9806675 254.9306675
[9511] 2.3556675 116.6306675 -77.1193325 152.9556675 16.0806675
[9516] -78.1193325 -47.8943325 -12.2693325 38.6056675 -28.8943325
[9521] 293.5556675 15.5556675 88.6056675 122.3556675 -115.5193325
[9526] -10.0443325 63.3806675 -115.1443325 -63.6193325 37.2056675
[9531] -39.8943325 184.9056675 -169.5193325 -131.5943325 127.4806675
[9536] -57.5693325 -76.5193325 -142.1693325 -12.5943325 -81.3193325
[9541] -37.8943325 303.2556675 -0.3693325 305.3056675 49.4806675
[9546] 302.9056675 64.5556675 50.8306675 98.8556675 -145.8693325
[9551] 7.1306675 93.4306675 23.5556675 -70.2443325 84.1056675
[9556] -52.3943325 142.4056675 98.0556675 17.7806675 -191.4193325
[9561] -96.1193325 124.3056675 227.3806675 -65.6943325 56.1056675
[9566] 16.5306675 137.8806675 5.7306675 -51.7943325 2.2056675
[9571] -300.9693325 -35.4693325 -93.6443325 38.8556675 -10.6193325
[9576] 104.9306675 -86.5443325 -66.4693325 -191.8443325 107.5056675
[9581] 151.7306675 8.0806675 166.2306675 62.1306675 21.7056675
[9586] -54.5943325 -146.2193325 -78.9943325 -124.7193325 87.5306675
[9591] 15.6806675 144.5306675 -6.4943325 -17.7943325 -269.7693325
[9596] -27.2693325 93.8056675 -38.7443325 -30.5693325 -36.2193325
[9601] 137.5056675 51.0556675 86.0056675 -118.0443325 28.8306675
[9606] -154.0193325 -152.5193325 -36.4193325 20.3306675 -66.4943325
[9611] 71.0556675 116.9556675 -20.0943325 -30.2443325 -123.7943325
[9616] 122.8806675 69.7056675 21.4056675 91.5556675 126.5056675
[9621] 196.9556675 -93.7443325 23.1056675 33.0806675 140.7556675
[9626] -41.2193325 -204.7193325 14.2306675 -6.5943325 65.7556675
[9631] 56.3556675 118.5056675 -209.2193325 -110.3943325 26.8556675
[9636] 24.5806675 63.1556675 -54.2193325 -183.7193325 215.2056675
[9641] -29.2943325 79.9056675 -140.2443325 -51.8443325 33.4806675
[9646] -210.0193325 -21.7943325 -71.5943325 61.2806675 -28.0943325
[9651] 59.6806675 98.9306675 73.9556675 32.6306675 5.3306675
[9656] -113.5443325 82.9056675 363.2556675 6.1056675 -59.6943325
[9661] 43.8806675 269.9806675 -43.8193325 335.0056675 20.7306675
[9666] 73.4806675 -199.9693325 24.2806675 21.7806675 -67.2443325
[9671] -7.9193325 95.1556675 -57.6443325 -72.4693325 276.9056675
[9676] 7.6056675 -38.9943325 -144.0443325 -179.2443325 -57.9693325
[9681] 155.0306675 -24.6943325 162.4306675 8.2056675 -52.4443325
[9686] -22.0193325 -4.8193325 -80.7193325 -36.0443325 45.1306675
[9691] 123.8056675 192.2306675 22.0806675 -81.2693325 -113.5693325
[9696] -6.0943325 -96.1193325 -73.0693325 42.9306675 113.2806675
[9701] -61.4943325 -30.1443325 32.3806675 189.6056675 166.5056675
[9706] 64.3556675 -58.7443325 -61.6193325 -51.0443325 -90.7443325
[9711] -125.6443325 -78.3943325 -61.3443325 -140.9693325 -75.9943325
[9716] 73.2556675 289.9056675 -39.3193325 -124.5943325 -180.2443325
[9721] -94.6193325 -15.8443325 40.5806675 -216.4443325 -75.4443325
[9726] -58.1193325 -71.9693325 -130.3443325 46.1056675 -147.5193325
[9731] -141.0693325 89.5806675 80.8056675 -26.5943325 -33.4443325
[9736] -37.6693325 71.7306675 -35.3443325 -104.2193325 -62.4693325
[9741] 91.1306675 -2.4443325 -146.1943325 67.0306675 -67.7193325
[9746] -43.4693325 -36.0193325 64.7556675 -5.1943325 16.7306675
[9751] -159.6943325 68.2556675 -48.2443325 -125.8943325 -81.1193325
[9756] -212.0443325 -128.6693325 -18.2943325 122.7056675 6.8556675
[9761] 108.2556675 -65.6443325 -12.8943325 -172.3443325 -83.0693325
[9766] -54.1943325 191.6806675 -179.1943325 84.7806675 20.1056675
[9771] -240.0693325 -13.5693325 51.4056675 46.3056675 55.7056675
[9776] 42.1306675 26.5306675 59.6556675 203.8306675 -62.8943325
[9781] 22.6306675 -11.6943325 -24.9693325 30.4056675 -34.2443325
[9786] -142.6693325 -43.2693325 65.3806675 100.5306675 -229.1693325
[9791] 85.4306675 -55.7943325 69.3806675 -118.9443325 -231.2443325
[9796] 14.5306675 207.4556675 51.3806675 -176.9943325 -0.1693325
[9801] 102.8806675 138.2306675 45.4806675 -152.1443325 9.4306675
[9806] -54.9693325 75.5556675 -367.2943325 63.3056675 -2.4193325
[9811] 204.0056675 -85.5943325 89.7306675 78.8306675 -199.7443325
[9816] -171.1443325 31.3306675 20.7056675 25.8306675 -88.0443325
[9821] -26.8443325 -70.6443325 -129.0693325 5.1056675 91.2806675
[9826] -81.9693325 53.2556675 -54.4943325 -114.9443325 -101.5193325
[9831] -85.5943325 -95.6443325 -39.7193325 100.9056675 79.0306675
[9836] 255.4806675 57.8556675 180.9556675 -19.0693325 128.6056675
[9841] 46.4806675 55.9806675 177.5056675 -144.3193325 -137.9943325
[9846] 26.0556675 9.2056675 170.8056675 -104.7943325 -24.9693325
[9851] -16.3943325 53.1056675 -225.3693325 38.5806675 -273.6193325
[9856] 0.3806675 -92.3943325 41.1556675 -223.5693325 7.8556675
[9861] 179.2806675 -31.5443325 46.2556675 -5.2693325 194.4556675
[9866] 11.5556675 -187.6193325 121.7556675 -110.0693325 109.8306675
[9871] 81.8306675 -86.1443325 147.0806675 -0.7943325 -70.8943325
[9876] -110.8193325 -51.2693325 96.5806675 50.4056675 -2.8693325
[9881] -107.1443325 50.8056675 -96.8443325 -1.4193325 130.4056675
[9886] -8.6193325 127.7556675 -5.7943325 106.8306675 -146.1693325
[9891] -34.9943325 87.2056675 -11.4193325 -229.5943325 114.2306675
[9896] -28.4943325 71.0806675 -62.1943325 200.5056675 64.5806675
[9901] -58.2943325 -29.6693325 57.5306675 -156.9693325 8.8556675
[9906] -53.3443325 -24.5443325 -7.7443325 47.5556675 124.0556675
[9911] -113.4693325 112.4806675 -58.6693325 -158.4943325 35.2806675
[9916] 105.3556675 45.1806675 -75.2943325 -61.5443325 -87.9193325
[9921] 37.6806675 82.6556675 -105.1443325 -1.9193325 68.9306675
[9926] 167.4556675 -65.0943325 -4.8193325 36.9806675 229.8556675
[9931] 76.8806675 30.2306675 -229.2443325 50.9306675 130.6306675
[9936] -131.9443325 49.7306675 17.6056675 17.7056675 18.2306675
[9941] 7.5806675 19.5306675 -77.6443325 -140.8193325 61.1806675
[9946] 145.6556675 60.0556675 31.8556675 132.9306675 -75.8943325
[9951] 308.7306675 158.2556675 70.7806675 -41.8193325 -138.7943325
[9956] 135.4306675 -49.4443325 33.1806675 14.4056675 0.9306675
[9961] 119.7806675 69.5556675 143.4306675 56.4056675 239.5056675
[9966] 67.2556675 -30.5943325 31.9556675 73.7556675 75.9806675
[9971] 318.6556675 39.0056675 -38.1693325 -25.8193325 -245.0193325
[9976] 47.0806675 -141.8943325 52.2806675 3.5556675 66.3556675
[9981] 109.6806675 94.1056675 -127.7943325 -115.1693325 45.4806675
[9986] -177.4443325 -78.5193325 5.5306675 -180.1443325 -58.8193325
[9991] 25.1056675 -83.4443325 96.5056675 53.8806675 -43.3443325
[9996] -168.4693325 252.2556675 -177.9443325 69.6056675 196.2306675abs((boyDifference - difference) / (sd(difference)*100)) [1] 4.922613e-03 1.325431e-03 9.172202e-03 6.441919e-03 1.464841e-02
[6] 1.615887e-03 9.058254e-03 6.803872e-03 2.873783e-03 1.134168e-02
[11] 5.310363e-03 1.158197e-02 9.493938e-03 5.863242e-03 1.055075e-02
[16] 7.032899e-04 1.332125e-02 9.013569e-03 7.440640e-03 8.584588e-03
[21] 3.188816e-03 9.664964e-03 9.002397e-03 1.270459e-02 9.123048e-03
[26] 5.112526e-03 3.010074e-03 2.322802e-02 3.888144e-03 5.490118e-03
[31] 2.238245e-02 1.231136e-02 9.708428e-03 1.110384e-02 9.575593e-03
[36] 3.335265e-03 7.780340e-04 9.245933e-03 3.200077e-04 3.791057e-03
[41] 1.373682e-02 9.660495e-03 3.182327e-02 1.038765e-02 6.901167e-03
[46] 3.759777e-03 6.197370e-03 1.953262e-03 6.115715e-03 2.470601e-03
[51] 7.105499e-03 8.777957e-03 3.631202e-03 9.917437e-03 6.760407e-03
[56] 9.333301e-05 8.539993e-04 2.307499e-03 7.285462e-03 6.146995e-03
[61] 2.145410e-03 1.273140e-02 5.243335e-03 4.118274e-03 8.343287e-03
[66] 5.060125e-03 8.115481e-04 3.856864e-03 1.590297e-03 4.348404e-03
[71] 1.091839e-02 7.456280e-03 3.689293e-03 1.691852e-03 4.217803e-03
[76] 6.239821e-03 1.156848e-03 8.115391e-03 6.982614e-03 2.306278e-03
[81] 3.003371e-03 1.103011e-02 5.064593e-03 1.582039e-02 1.764234e-02
[86] 1.957731e-03 2.559972e-03 9.120814e-03 5.671095e-03 2.407827e-02
[91] 1.664585e-02 1.032831e-04 6.276583e-03 1.410000e-02 1.806807e-02
[96] 3.101679e-03 2.217913e-02 9.752101e-03 1.474001e-02 1.945210e-02
[101] 1.036653e-02 7.690969e-04 1.000904e-02 1.201765e-02 1.619676e-02
[106] 9.848084e-04 1.465633e-02 1.042685e-02 5.717001e-03 5.886806e-03
[111] 6.427501e-03 1.449537e-03 3.829040e-03 1.569527e-02 6.429735e-03
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[121] 8.038322e-04 1.262871e-03 1.444062e-02 4.379684e-03 2.322701e-02
[126] 5.004268e-03 5.412909e-05 1.120438e-02 1.178306e-02 3.081571e-03
[131] 1.404739e-02 4.657955e-03 1.738772e-03 2.925172e-03 1.173491e-02
[136] 6.831904e-03 1.547631e-02 4.620986e-03 1.144121e-02 1.243993e-02
[141] 8.742209e-03 2.450492e-03 1.888236e-02 5.401969e-03 9.297322e-03
[146] 5.777327e-03 1.906342e-03 8.801313e-03 1.260405e-02 6.207320e-03
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[156] 1.521043e-02 2.447597e-02 5.005281e-03 1.415362e-02 4.103855e-03
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[166] 1.453121e-02 2.696263e-03 6.570494e-03 8.584588e-03 1.555228e-02
[171] 1.245334e-02 2.763291e-03 1.243100e-02 7.466438e-03 2.505128e-03
[176] 7.384783e-03 6.797259e-04 1.553988e-02 2.997890e-03 1.422166e-02
[181] 1.098095e-02 9.517502e-03 8.540893e-05 1.362857e-02 7.845043e-03
[186] 2.111896e-03 1.417474e-02 4.980704e-03 3.442510e-03 5.400747e-03
[191] 6.095607e-03 7.386004e-03 4.865653e-04 5.323769e-03 4.447934e-03
[196] 8.304291e-03 1.218177e-02 7.556912e-04 1.716429e-03 5.835418e-03
[201] 7.784718e-03 1.274034e-02 9.813439e-03 5.673329e-03 1.450887e-02
[206] 2.562662e-02 1.409553e-02 1.041121e-02 1.086364e-03 4.075823e-03
[211] 9.277213e-03 1.239301e-02 2.782178e-03 6.267646e-03 9.681617e-03
[216] 1.803902e-02 9.079584e-03 1.435795e-02 3.458707e-02 9.549795e-03
[221] 8.798066e-03 1.696321e-03 5.156198e-03 1.459032e-02 1.240073e-02
[226] 4.848882e-03 8.505376e-03 9.698478e-03 6.641991e-03 8.307538e-03
[231] 9.433702e-04 1.524273e-02 1.595993e-02 8.957712e-03 3.766480e-03
[236] 3.324094e-03 1.003240e-02 2.271414e-02 8.193590e-03 1.900870e-02
[241] 3.020912e-02 3.335265e-03 5.308129e-03 3.146365e-03 5.326003e-03
[246] 1.566724e-02 9.253857e-03 3.211159e-03 7.256416e-03 2.147644e-03
[251] 1.405865e-03 1.401733e-02 6.665347e-03 4.482461e-03 6.781529e-03
[256] 4.561882e-03 9.311949e-03 7.091080e-03 1.914276e-02 1.563941e-02
[261] 6.188433e-03 6.311318e-03 6.570494e-03 3.108382e-03 8.852701e-03
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[271] 2.401338e-03 8.722100e-03 1.984980e-02 8.927653e-03 7.688644e-03
[276] 1.244997e-03 1.524049e-02 2.245952e-03 1.388876e-02 5.702374e-03
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[291] 3.530660e-03 4.971767e-03 1.591870e-02 6.817277e-03 7.707740e-03
[296] 3.101679e-03 3.108382e-03 2.049327e-02 8.229339e-03 1.215171e-02
[301] 3.141896e-03 7.322454e-05 2.761056e-03 6.137045e-03 3.356476e-04
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[981] 7.239555e-03 1.017214e-02 7.569125e-04 6.158166e-03 2.263147e-02
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[1011] 7.502096e-04 1.423852e-02 3.619018e-03 3.558692e-03 5.633112e-03
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[1886] 1.579683e-02 5.259988e-03 1.259958e-02 3.860229e-04 1.891486e-02
[1891] 6.306619e-05 1.737544e-02 1.118305e-02 2.824629e-03 9.371053e-03
[1896] 5.113747e-03 2.101946e-03 2.641419e-03 1.069943e-02 2.139928e-03
[1901] 1.281967e-03 7.199338e-03 1.394807e-02 7.835093e-03 1.321299e-02
[1906] 5.893509e-03 1.261197e-02 1.119878e-03 1.873388e-02 1.276390e-02
[1911] 9.405788e-03 3.818881e-03 1.281184e-02 1.664808e-02 1.224880e-02
[1916] 1.062570e-02 1.178407e-02 9.805723e-03 1.068490e-03 3.420167e-03
[1921] 5.051188e-03 1.190818e-02 8.935369e-03 1.632858e-02 5.330472e-03
[1926] 3.906018e-03 2.340923e-04 9.863814e-03 8.840517e-03 2.309072e-02
[1931] 6.915585e-03 4.771903e-03 1.649737e-02 1.512207e-02 5.185244e-03
[1936] 7.850733e-03 4.783075e-03 5.266691e-03 1.355138e-02 2.036368e-02
[1941] 1.162219e-02 6.734609e-03 5.646518e-03 3.737434e-03 1.089381e-02
[1946] 3.890378e-03 5.657779e-04 5.929257e-03 2.889423e-03 1.003809e-02
[1951] 2.395739e-04 4.508259e-03 1.627496e-02 5.552678e-03 2.578972e-02
[1956] 5.567305e-03 2.466689e-02 1.429215e-02 2.299575e-03 1.995156e-02
[1961] 2.463898e-03 2.768662e-02 2.669451e-03 1.222422e-02 9.535286e-04
[1966] 2.607571e-02 7.049642e-03 7.218434e-03 2.510818e-03 9.461645e-03
[1971] 2.216997e-04 4.557413e-03 6.857494e-03 8.040647e-03 4.041296e-03
[1976] 4.599864e-03 1.131386e-02 4.716046e-03 1.706142e-02 3.005605e-03
[1981] 5.134869e-03 1.281967e-03 5.864463e-03 8.320944e-03 1.141988e-02
[1986] 3.024701e-03 7.625072e-03 8.753290e-04 1.378041e-03 5.388563e-03
[1991] 1.066145e-02 1.357819e-02 9.043746e-04 7.868607e-03 1.063911e-02
[1996] 6.220726e-03 1.342972e-02 9.640387e-03 2.749885e-03 1.375815e-02
[2001] 1.670641e-04 2.517521e-03 1.484848e-02 1.179747e-02 1.636108e-02
[2006] 1.499025e-02 1.031961e-02 6.037516e-03 8.943293e-03 6.611724e-03
[2011] 2.048109e-02 1.510095e-02 1.042238e-02 1.383513e-02 1.285998e-02
[2016] 8.229339e-03 2.506582e-02 1.374251e-02 2.697490e-02 6.478889e-03
[2021] 5.267912e-03 1.527970e-02 1.179100e-04 1.145340e-02 2.088540e-03
[2026] 6.344832e-03 2.272978e-02 1.031392e-02 1.110038e-02 5.981889e-05
[2031] 9.850409e-03 1.478583e-03 2.160037e-03 4.786412e-04 3.222420e-04
[2036] 7.150184e-03 1.408314e-02 5.847602e-03 1.472893e-03 6.463249e-03
[2041] 1.000448e-03 3.462619e-03 3.459163e-03 9.512943e-04 4.061314e-04
[2046] 7.727848e-03 3.976502e-03 1.031392e-02 3.664716e-03 3.015764e-03
[2051] 8.379035e-03 1.471880e-03 1.035759e-02 9.660495e-03 1.951689e-02
[2056] 1.891924e-03 1.270796e-03 1.589513e-02 1.503160e-03 1.302186e-02
[2061] 1.137865e-02 9.553250e-03 6.361485e-03 8.946541e-03 5.907928e-03
[2066] 1.118650e-02 1.104006e-02 2.379776e-02 1.171603e-02 1.005373e-02
[2071] 1.347440e-02 1.989011e-03 2.057260e-03 9.046070e-03 7.581399e-03
[2076] 1.823341e-02 1.863891e-03 1.043010e-02 3.286111e-03 1.865112e-03
[2081] 2.304380e-02 4.762966e-03 8.097516e-03 5.929257e-03 3.293827e-03
[2086] 1.156410e-02 1.957722e-02 1.041222e-02 1.072958e-03 1.212704e-03
[2091] 3.136415e-03 1.924217e-03 3.424636e-03 1.410771e-02 1.276614e-02
[2096] 7.971294e-04 9.216888e-03 8.647148e-03 9.734226e-03 1.299180e-02
[2101] 3.473790e-03 7.643959e-03 1.174722e-03 1.017438e-02 2.634716e-03
[2106] 1.349999e-02 2.043854e-03 1.417036e-03 6.857494e-03 4.820967e-04
[2111] 8.472874e-03 1.029056e-02 1.052850e-03 1.491774e-02 1.344759e-02
[2116] 3.569864e-03 1.452451e-02 7.209497e-03 1.491899e-04 3.177735e-04
[2121] 1.017101e-03 1.309234e-02 8.901855e-03 1.119422e-02 2.246289e-02
[2126] 1.613420e-02 1.472893e-03 8.798066e-03 7.746735e-03 1.092054e-03
[2131] 2.563219e-03 1.938754e-04 1.223316e-02 1.637002e-02 4.364044e-03
[2136] 1.036530e-02 5.162901e-03 1.488870e-02 1.528640e-02 4.909207e-03
[2141] 1.325544e-02 2.252655e-03 5.146040e-03 1.364635e-03 8.183640e-03
[2146] 4.224506e-03 5.532570e-03 5.112526e-03 5.674550e-03 1.996935e-03
[2151] 4.208866e-03 4.334999e-03 6.582678e-03 1.015305e-02 1.674091e-02
[2156] 8.034957e-03 1.846678e-02 6.266633e-03 1.623811e-03 8.092035e-03
[2161] 9.581075e-03 3.325107e-03 1.163336e-02 7.110057e-04 1.157181e-02
[2166] 1.010489e-04 4.014484e-03 1.409321e-03 7.643959e-03 3.267015e-03
[2171] 1.853056e-02 1.889028e-02 1.117980e-02 1.445078e-02 1.686603e-02
[2176] 8.913027e-03 9.299646e-04 6.249772e-03 1.015752e-02 5.412009e-04
[2181] 2.374313e-02 6.409626e-03 5.995064e-03 4.933784e-03 2.464911e-03
[2186] 1.541030e-02 6.858715e-03 4.345157e-03 1.104676e-02 6.288976e-03
[2191] 1.216959e-02 6.688911e-03 5.845368e-03 5.621941e-03 2.402351e-03
[2196] 9.344241e-03 8.550061e-03 1.217173e-03 5.892288e-03 1.881855e-04
[2201] 1.395802e-02 7.324458e-03 1.342292e-03 9.014790e-03 6.134811e-03
[2206] 4.369734e-03 6.046453e-03 4.255786e-03 8.119859e-03 1.218969e-02
[2211] 1.018332e-02 6.683221e-03 6.600553e-03 7.569125e-04 1.173837e-02
[2216] 7.960213e-03 1.297270e-02 7.601508e-03 5.205353e-03 9.267263e-03
[2221] 1.856956e-02 1.030507e-03 2.954217e-03 1.388998e-02 7.566980e-03
[2226] 4.317214e-04 9.433702e-04 6.253227e-03 2.645887e-03 1.129375e-02
[2231] 9.403554e-03 3.825674e-04 1.862765e-02 2.937564e-03 2.406364e-02
[2236] 9.165499e-03 1.861201e-02 6.878824e-03 4.626675e-03 9.922918e-03
[2241] 2.698497e-03 4.664568e-04 4.008795e-03 5.798448e-03 1.362064e-02
[2246] 8.618102e-03 1.238294e-03 2.245049e-02 8.417018e-03 9.002397e-03
[2251] 1.498692e-03 1.384630e-02 4.339557e-04 1.206002e-03 3.830053e-03
[2256] 1.067477e-03 6.942397e-03 3.024701e-03 3.915045e-04 3.290579e-03
[2261] 4.481448e-03 5.758462e-05 6.917820e-03 5.455591e-03 6.524587e-03
[2266] 8.123315e-03 4.485916e-03 8.732050e-03 7.715456e-03 8.379035e-03
[2271] 5.499055e-03 1.614984e-02 1.779102e-02 5.711312e-03 5.969474e-03
[2276] 2.133225e-03 1.076524e-02 1.381949e-02 4.769669e-03 3.044809e-03
[2281] 1.791390e-02 5.215303e-03 6.083422e-03 1.298620e-03 2.015912e-04
[2286] 8.146670e-03 1.055084e-03 7.499952e-03 2.066653e-02 5.256741e-03
[2291] 1.870037e-02 2.062062e-02 3.011205e-04 1.752514e-02 1.368767e-02
[2296] 7.620603e-03 1.145563e-02 2.636950e-03 5.739344e-03 3.588751e-03
[2301] 3.736303e-04 1.443839e-02 1.574666e-02 5.687956e-03 1.249466e-03
[2306] 1.235604e-02 2.009557e-02 2.452637e-04 8.367864e-03 1.561707e-02
[2311] 1.051500e-02 2.743092e-04 1.425294e-02 1.384744e-03 1.038431e-03
[2316] 1.520596e-02 8.872810e-03 3.106148e-03 7.663054e-03 1.946559e-03
[2321] 4.548476e-03 8.067458e-03 8.621558e-03 1.463622e-02 1.637774e-02
[2326] 2.628013e-03 1.653860e-02 8.191356e-03 1.642698e-03 6.886630e-04
[2331] 6.227429e-03 2.082618e-02 6.608477e-03 4.704875e-03 5.127153e-03
[2336] 4.188758e-03 1.943312e-03 2.015143e-02 5.722483e-03 1.155170e-02
[2341] 1.174722e-03 1.172374e-02 1.829373e-02 1.096531e-02 7.841796e-03
[2346] 1.835060e-02 7.473141e-03 5.172851e-03 1.336269e-02 7.593792e-03
[2351] 4.641325e-05 1.331130e-02 7.663054e-03 2.030458e-02 6.981601e-03
[2356] 1.411889e-02 3.347449e-03 9.425897e-03 1.105692e-02 4.206632e-03
[2361] 5.903549e-04 5.542728e-03 4.694717e-03 5.828715e-03 5.962771e-03
[2366] 2.324366e-02 2.204061e-02 1.649291e-02 1.303088e-03 1.192596e-03
[2371] 8.176937e-03 2.935339e-02 7.754659e-03 1.020342e-02 6.995006e-03
[2376] 1.744349e-02 1.032184e-02 4.594174e-03 1.048941e-02 1.465633e-02
[2381] 1.509872e-02 1.141095e-02 1.023804e-03 1.033962e-03 5.099210e-04
[2386] 2.184614e-03 1.077987e-02 6.586134e-03 1.326986e-02 9.028196e-03
[2391] 1.053186e-02 1.133945e-02 1.294041e-02 4.346170e-03 7.080922e-03
[2396] 8.266308e-03 1.740226e-02 8.691833e-03 2.188969e-02 2.641509e-04
[2401] 1.797423e-02 1.160095e-03 6.712266e-03 1.564498e-03 1.372118e-02
[2406] 8.968883e-03 1.231258e-02 5.446564e-04 3.467087e-03 1.765583e-03
[2411] 4.942811e-04 1.269118e-02 1.309904e-02 7.322223e-03 1.378497e-02
[2416] 6.478889e-03 9.023727e-03 6.183965e-03 2.444803e-03 1.036977e-02
[2421] 5.886806e-03 3.242438e-03 6.329192e-03 2.686104e-03 5.203118e-03
[2426] 5.675563e-03 2.968844e-03 1.824234e-02 1.367772e-02 1.470996e-02
[2431] 6.861963e-03 3.557471e-03 8.184653e-03 6.798390e-03 1.521815e-02
[2436] 2.839256e-03 1.567069e-02 9.870517e-03 1.289914e-05 2.741961e-03
[2441] 1.126348e-02 6.423032e-03 6.445375e-03 1.677544e-02 7.453032e-03
[2446] 1.537455e-02 1.220310e-02 1.111155e-02 4.848882e-03 2.764304e-03
[2451] 8.808016e-03 1.148914e-02 8.430587e-06 1.837640e-02 6.819602e-04
[2456] 1.193377e-02 1.325431e-03 1.286221e-02 5.995064e-03 1.418145e-02
[2461] 1.200973e-02 1.410000e-02 5.326003e-03 2.828085e-03 3.051512e-03
[2466] 8.557777e-03 1.882987e-03 3.398838e-03 6.079967e-03 7.024052e-03
[2471] 6.352548e-03 1.017661e-02 1.927234e-02 4.384153e-03 6.079967e-03
[2476] 8.122093e-03 2.678844e-02 1.719223e-02 2.153334e-03 2.082850e-03
[2481] 3.909473e-03 3.077102e-03 1.100207e-02 1.662249e-02 7.412725e-04
[2486] 1.452451e-02 1.817633e-02 1.013517e-02 1.156857e-02 1.042900e-03
[2491] 1.866126e-03 9.481753e-03 1.669509e-03 6.495542e-03 3.503849e-03
[2496] 1.210926e-02 1.829364e-03 3.646842e-03 1.631863e-02 3.289358e-03
[2501] 5.934739e-03 1.055867e-02 7.564746e-03 1.522607e-02 1.546624e-03
[2506] 3.907239e-03 1.310229e-02 3.389901e-03 4.155244e-03 7.169280e-03
[2511] 1.006043e-02 1.086578e-02 1.559127e-02 1.195733e-02 2.802286e-03
[2516] 5.844355e-03 1.711180e-02 8.114378e-03 1.723793e-02 2.820161e-03
[2521] 3.404527e-03 2.254889e-03 1.256505e-02 1.058772e-02 1.092054e-03
[2526] 1.734071e-02 1.352132e-02 1.981751e-02 9.647000e-04 5.938104e-04
[2531] 3.384419e-03 1.288455e-02 1.818193e-03 6.448622e-03 8.376801e-03
[2536] 1.231806e-02 3.655779e-03 4.918144e-03 6.360472e-03 1.583594e-03
[2541] 2.171208e-03 9.439302e-03 4.326061e-03 6.344832e-03 1.110160e-02
[2546] 1.822670e-02 9.011335e-03 1.961073e-02 5.475700e-03 6.663202e-04
[2551] 2.606108e-02 1.024689e-02 1.055745e-02 1.081895e-03 8.809237e-03
[2556] 5.671095e-03 1.102340e-02 2.817926e-03 5.494587e-03 1.774288e-02
[2561] 6.685455e-03 9.902900e-04 1.768601e-02 1.365648e-03 8.378022e-03
[2566] 6.097841e-03 8.887436e-03 1.016768e-02 5.822012e-03 1.092286e-02
[2571] 9.846953e-03 6.548151e-03 1.975149e-02 6.072161e-04 1.999178e-02
[2576] 1.006815e-02 6.018628e-03 1.548859e-03 8.984523e-03 5.205353e-03
[2581] 1.162329e-03 8.184653e-03 8.664009e-03 1.100106e-02 5.331485e-03
[2586] 8.551074e-03 8.612621e-03 9.986699e-03 5.670082e-03 1.017316e-02
[2591] 1.234487e-02 7.012880e-03 1.068603e-02 8.020538e-03 1.058102e-02
[2596] 1.662807e-03 1.041121e-02 2.084071e-03 2.253876e-03 6.953658e-04
[2601] 6.407302e-04 1.738772e-03 1.172487e-03 9.338760e-03 4.437775e-03
[2606] 1.168019e-03 1.298510e-02 1.100553e-02 1.671744e-03 1.909798e-03
[2611] 2.155455e-02 3.266002e-03 3.569864e-03 3.961875e-03 7.369143e-03
[2616] 1.299850e-02 3.608859e-03 4.330530e-03 9.516281e-03 1.769819e-02
[2621] 3.234633e-04 6.777060e-03 5.239880e-03 3.650298e-03 1.696210e-02
[2626] 1.964648e-02 1.680672e-02 1.036754e-02 1.561037e-02 6.474420e-03
[2631] 6.439775e-04 4.859040e-03 5.630878e-03 1.924217e-03 1.021460e-02
[2636] 4.939474e-03 6.946865e-03 2.637611e-02 2.643653e-03 9.047083e-03
[2641] 4.014484e-03 1.136748e-02 1.472893e-03 8.445050e-03 1.817308e-02
[2646] 1.397264e-02 7.688644e-03 1.002021e-02 3.807710e-03 1.152936e-02
[2651] 1.062570e-02 1.631071e-02 1.353464e-03 4.696951e-03 1.016199e-02
[2656] 3.358621e-03 4.021187e-03 8.161297e-03 5.076868e-04 1.475119e-02
[2661] 1.059553e-03 2.025542e-02 6.416329e-03 4.977457e-03 1.432891e-02
[2666] 9.240452e-03 4.413198e-03 8.459469e-03 1.311915e-02 1.736651e-02
[2671] 2.418998e-02 1.437145e-03 1.576677e-02 2.731780e-05 3.237970e-03
[2676] 2.167297e-02 9.061710e-03 5.979424e-03 9.256092e-03 5.036561e-03
[2681] 1.071385e-02 1.963876e-02 3.919424e-03 6.093372e-03 1.129253e-02
[2686] 7.889729e-03 1.605153e-02 2.217913e-02 1.295706e-02 1.810036e-02
[2691] 3.369792e-03 3.412243e-03 9.367805e-03 1.858410e-03 1.183322e-02
[2696] 4.927081e-03 8.662788e-03 7.725524e-04 6.359251e-03 4.065873e-03
[2701] 3.980970e-03 2.193661e-02 1.796529e-02 4.832229e-03 1.221975e-02
[2706] 8.734285e-03 1.817856e-02 2.067547e-02 1.059219e-02 3.065931e-03
[2711] 4.437775e-03 4.566350e-03 1.941078e-03 6.960271e-03 1.722798e-02
[2716] 2.435633e-02 4.664568e-04 3.194506e-03 2.167419e-02 7.065372e-04
[2721] 1.824896e-03 7.180451e-03 6.289989e-03 8.572404e-03 4.463483e-04
[2726] 1.463956e-03 4.361900e-04 1.974378e-02 7.618369e-03 2.126523e-03
[2731] 8.190343e-03 3.118540e-03 1.359607e-02 1.965765e-02 9.432599e-03
[2736] 2.533160e-03 3.793291e-03 9.400098e-03 2.641419e-03 7.216199e-03
[2741] 1.193823e-02 1.104798e-02 4.549489e-03 1.302633e-02 1.459488e-03
[2746] 1.406303e-02 1.406425e-02 5.200794e-04 6.072161e-04 6.418563e-03
[2751] 9.135441e-03 5.568408e-04 5.107044e-03 5.080233e-03 9.737474e-03
[2756] 1.468863e-02 8.294133e-03 3.054759e-03 6.303394e-03 7.161355e-03
[2761] 7.112201e-03 8.880734e-03 1.046147e-03 7.202794e-03 1.999169e-03
[2766] 9.735239e-03 8.944306e-03 1.519581e-02 1.168129e-02 1.063017e-02
[2771] 2.569922e-03 1.665041e-03 1.126125e-02 1.356255e-02 1.193600e-02
[2776] 7.173748e-03 1.761228e-02 1.164778e-02 2.159924e-02 7.642946e-03
[2781] 1.674314e-02 9.456045e-04 4.837710e-03 1.252585e-02 9.403554e-03
[2786] 6.601774e-03 7.823922e-03 3.954159e-03 2.377095e-02 2.732011e-03
[2791] 1.598573e-02 9.423572e-04 4.290313e-03 9.044849e-03 3.438042e-03
[2796] 3.421180e-03 3.262547e-03 3.261534e-03 1.176956e-03 8.923185e-03
[2801] 7.412815e-03 1.709717e-02 3.512876e-04 9.081818e-03 1.160756e-02
[2806] 7.569125e-04 1.938844e-03 5.346112e-03 1.649514e-02 1.127588e-02
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[9226] 4.214348e-03 4.486929e-03 3.770948e-03 6.893243e-03 3.413375e-04
[9231] 2.573377e-03 9.614589e-03 1.200750e-02 1.046585e-02 1.042462e-02
[9236] 1.581270e-04 2.892879e-03 1.019449e-02 3.196740e-03 5.985114e-03
[9241] 3.827818e-03 3.966343e-03 2.013579e-02 2.835801e-03 9.352166e-03
[9246] 8.398130e-03 4.595396e-03 9.989947e-03 4.500335e-03 1.577672e-02
[9251] 5.769493e-04 1.018209e-02 7.344566e-03 8.651616e-03 2.057260e-03
[9256] 4.663437e-03 1.255156e-03 1.511761e-02 1.048596e-02 1.132271e-03
[9261] 5.312508e-04 5.702374e-03 9.279447e-03 9.395630e-03 1.056984e-02
[9266] 6.382815e-03 1.819206e-03 9.835782e-03 8.540893e-05 9.297322e-03
[9271] 5.410906e-03 2.255226e-02 1.035089e-02 9.019259e-03 1.522047e-03
[9276] 3.987673e-03 8.440492e-04 5.557147e-03 1.355707e-02 1.624145e-02
[9281] 3.186582e-03 4.034593e-03 7.971384e-03 1.186906e-03 1.659792e-02
[9286] 2.027655e-02 6.150451e-03 3.096198e-03 7.251948e-03 1.417036e-03
[9291] 2.299342e-02 3.389901e-03 3.588751e-03 1.678336e-02 1.153392e-03
[9296] 3.277174e-03 1.565729e-02 1.255165e-02 1.247232e-03 9.726302e-03
[9301] 2.492607e-02 4.831007e-03 3.058215e-03 2.566675e-03 6.770357e-03
[9306] 2.274765e-02 1.973371e-03 5.426546e-03 1.983529e-03 5.274615e-03
[9311] 2.602423e-03 8.693055e-03 1.300854e-03 8.317697e-03 9.662730e-03
[9316] 3.925113e-03 1.366431e-02 6.368188e-03 4.426604e-03 1.175178e-02
[9321] 5.939207e-03 4.056936e-03 4.195461e-03 2.162181e-04 7.040705e-03
[9326] 1.269574e-03 4.138472e-04 6.004001e-03 7.882013e-03 1.353249e-02
[9331] 4.661203e-03 5.079012e-03 5.959316e-03 8.045115e-03 1.063240e-02
[9336] 1.375246e-02 1.044919e-02 4.942811e-04 9.602314e-04 6.809471e-04
[9341] 2.192330e-03 1.792609e-02 1.341509e-02 1.151047e-02 4.741727e-04
[9346] 8.916482e-03 1.675756e-02 2.594499e-03 1.016422e-02 7.638477e-03
[9351] 7.354724e-03 2.074798e-02 4.976235e-03 2.535395e-03 2.016707e-02
[9356] 1.570745e-02 9.803489e-03 1.707483e-02 6.749236e-03 4.399793e-03
[9361] 1.392450e-02 4.614283e-03 4.035606e-03 1.919191e-02 2.535395e-03
[9366] 6.783763e-03 1.992466e-03 7.721145e-03 5.265678e-03 7.466438e-03
[9371] 7.667523e-03 3.894847e-03 7.121139e-03 2.318580e-04 1.328887e-03
[9376] 3.541831e-03 1.582933e-02 1.407643e-02 6.007457e-03 4.795259e-03
[9381] 3.777651e-03 2.766651e-02 1.594765e-03 7.724393e-03 4.961817e-03
[9386] 1.682459e-02 8.267321e-03 4.997565e-03 5.862229e-03 7.261898e-03
[9391] 4.262399e-04 6.789453e-03 1.157527e-02 2.358896e-02 1.019002e-02
[9396] 1.283987e-02 8.756627e-03 3.554224e-03 1.668505e-02 1.691620e-02
[9401] 1.082008e-02 2.105193e-03 1.401286e-02 1.531097e-02 3.682590e-03
[9406] 1.393121e-02 3.309467e-03 3.311701e-03 1.090275e-02 7.412725e-04
[9411] 1.210134e-02 1.882427e-02 8.887436e-03 2.437087e-03 1.264650e-02
[9416] 2.530590e-02 1.508084e-02 1.923314e-02 2.687325e-03 8.224870e-03
[9421] 1.347774e-03 2.493623e-02 1.374585e-03 8.408081e-03 8.871797e-03
[9426] 9.327588e-03 1.122112e-03 1.959965e-03 1.132828e-02 3.770948e-03
[9431] 1.249680e-02 1.100654e-02 7.559056e-03 8.417018e-03 5.935960e-03
[9436] 1.283194e-02 8.240510e-03 9.622513e-03 3.941766e-03 1.581145e-02
[9441] 3.436820e-03 2.700731e-03 1.271800e-02 5.856539e-03 1.250687e-03
[9446] 6.172793e-03 6.787129e-04 3.452460e-03 8.250668e-03 1.654876e-02
[9451] 2.192330e-03 3.294610e-02 1.429092e-02 2.768772e-03 3.054759e-03
[9456] 1.722798e-02 1.027045e-02 1.176619e-02 1.405865e-03 5.737020e-04
[9461] 1.135854e-02 1.413351e-02 9.709649e-03 1.423182e-02 1.025025e-03
[9466] 1.735087e-02 1.112841e-02 4.312656e-03 5.592895e-03 4.984159e-03
[9471] 1.714186e-02 3.512876e-04 1.465958e-02 7.609432e-03 4.343936e-03
[9476] 2.563219e-03 9.944248e-03 4.434528e-03 6.620661e-03 5.987348e-03
[9481] 2.998993e-04 6.094504e-04 1.148143e-02 2.283256e-02 1.641685e-03
[9486] 1.125678e-02 1.924217e-03 9.530907e-03 6.896698e-03 4.674608e-03
[9491] 2.615829e-03 1.068826e-02 1.038887e-02 2.229299e-03 3.882662e-03
[9496] 1.717883e-02 9.423662e-03 4.026669e-03 2.429163e-03 6.217479e-03
[9501] 5.309142e-03 3.535218e-04 4.927081e-03 6.079967e-03 8.070795e-04
[9506] 3.122919e-04 5.507993e-03 1.210703e-02 2.663851e-04 2.278340e-02
[9511] 2.105283e-04 1.042340e-02 6.892230e-03 1.366980e-02 1.437145e-03
[9516] 6.981601e-03 4.280363e-03 1.096522e-03 3.450226e-03 2.582315e-03
[9521] 2.623535e-02 1.390225e-03 7.918774e-03 1.093504e-02 1.032407e-02
[9526] 8.976717e-04 5.664392e-03 1.029056e-02 5.685721e-03 3.325107e-03
[9531] 3.565395e-03 1.652520e-02 1.515011e-02 1.176071e-02 1.139307e-02
[9536] 5.145027e-03 6.838607e-03 1.270581e-02 1.125568e-03 7.267588e-03
[9541] 3.386653e-03 2.710225e-02 3.300760e-05 2.728546e-02 4.422135e-03
[9546] 2.707097e-02 5.769403e-03 4.542786e-03 8.834827e-03 1.303648e-02
[9551] 6.372747e-04 8.349989e-03 2.105193e-03 6.277804e-03 7.516605e-03
[9556] 4.682532e-03 1.272693e-02 8.763330e-03 1.589076e-03 1.710733e-02
[9561] 8.590278e-03 1.110932e-02 2.032123e-02 5.871166e-03 5.014218e-03
[9566] 1.477362e-03 1.232253e-02 5.121553e-04 4.628910e-03 1.971226e-04
[9571] 2.689792e-02 3.169929e-03 8.369085e-03 3.472569e-03 9.490600e-04
[9576] 9.377756e-03 7.734551e-03 5.940429e-03 1.714531e-02 9.607886e-03
[9581] 1.356032e-02 7.221771e-04 1.485620e-02 5.552678e-03 1.939857e-03
[9586] 4.879148e-03 1.306776e-02 7.059800e-03 1.114629e-02 7.822701e-03
[9591] 1.401396e-03 1.291685e-02 5.804048e-04 1.590297e-03 2.410955e-02
[9596] 2.437087e-03 8.383504e-03 3.462619e-03 2.732011e-03 3.236957e-03
[9601] 1.228901e-02 4.562895e-03 7.686410e-03 1.054974e-02 2.576625e-03
[9606] 1.376486e-02 1.363080e-02 3.254831e-03 1.816971e-03 5.942663e-03
[9611] 6.350314e-03 1.045244e-02 1.795850e-03 2.702965e-03 1.106362e-02
[9616] 1.098196e-02 6.229663e-03 1.913045e-03 8.182419e-03 1.130593e-02
[9621] 1.760212e-02 8.378022e-03 2.064976e-03 2.956451e-03 1.257947e-02
[9626] 3.683812e-03 1.829597e-02 1.271809e-03 5.893419e-04 5.876648e-03
[9631] 5.036561e-03 1.059097e-02 1.869813e-02 9.866049e-03 2.400117e-03
[9636] 2.196798e-03 5.644283e-03 4.845634e-03 1.641917e-02 1.923314e-02
[9641] 2.618063e-03 7.141247e-03 1.253377e-02 4.633378e-03 2.992200e-03
[9646] 1.876963e-02 1.947781e-03 6.398455e-03 5.476713e-03 2.510818e-03
[9651] 5.333719e-03 8.841530e-03 6.609490e-03 2.916234e-03 4.764069e-04
[9656] 1.014757e-02 7.409360e-03 3.246451e-02 5.456694e-04 5.334940e-03
[9661] 3.921658e-03 2.412843e-02 3.916176e-03 2.993978e-02 1.852720e-03
[9666] 6.567039e-03 1.787145e-02 2.169987e-03 1.946559e-03 6.009691e-03
[9671] 7.077584e-04 8.504154e-03 5.151730e-03 6.476655e-03 2.474733e-02
[9676] 6.797259e-04 3.484961e-03 1.287338e-02 1.601924e-02 5.180775e-03
[9681] 1.385524e-02 2.206956e-03 1.451659e-02 7.333485e-04 4.687001e-03
[9686] 1.967889e-03 4.307084e-04 7.213965e-03 3.221317e-03 4.033372e-03
[9691] 1.106463e-02 1.717984e-02 1.973371e-03 7.263119e-03 1.014980e-02
[9696] 5.446564e-04 8.590278e-03 6.530277e-03 3.836755e-03 1.012400e-02
[9701] 5.495808e-03 2.694028e-03 2.893892e-03 1.694524e-02 1.488077e-02
[9706] 5.751528e-03 5.250038e-03 5.506980e-03 4.561882e-03 8.109909e-03
[9711] 1.122896e-02 7.006178e-03 5.482403e-03 1.259857e-02 6.791687e-03
[9716] 6.546930e-03 2.590915e-02 3.514007e-03 1.113512e-02 1.610861e-02
[9721] 8.456222e-03 1.416023e-03 3.626734e-03 1.934384e-02 6.742533e-03
[9726] 5.194181e-03 6.431969e-03 1.164900e-02 4.120508e-03 1.318395e-02
[9731] 1.260750e-02 8.005911e-03 7.221681e-03 2.376761e-03 2.988952e-03
[9736] 3.366545e-03 6.410639e-03 3.158757e-03 9.314183e-03 5.582945e-03
[9741] 8.144436e-03 2.184524e-04 1.306553e-02 5.990596e-03 6.052142e-03
[9746] 3.884896e-03 3.219083e-03 5.787277e-03 4.642225e-04 1.495236e-03
[9751] 1.427204e-02 6.100075e-03 4.311643e-03 1.125130e-02 7.249713e-03
[9756] 1.895061e-02 1.149930e-02 1.634982e-03 1.096632e-02 6.126977e-04
[9761] 9.674914e-03 5.866698e-03 1.152379e-03 1.540258e-02 7.423987e-03
[9766] 4.843400e-03 1.713069e-02 1.601477e-02 7.576931e-03 1.796863e-03
[9771] 2.145523e-02 1.212704e-03 4.594174e-03 4.138382e-03 4.978470e-03
[9776] 3.765259e-03 2.371071e-03 5.331485e-03 1.821654e-02 5.620928e-03
[9781] 2.022525e-03 1.045134e-03 2.231533e-03 2.717384e-03 3.060449e-03
[9786] 1.275050e-02 3.867022e-03 5.843134e-03 8.984523e-03 2.048109e-02
[9791] 7.635022e-03 4.986394e-03 6.200618e-03 1.063017e-02 2.066653e-02
[9796] 1.298620e-03 1.854051e-02 4.591940e-03 1.581816e-02 1.513341e-05
[9801] 9.194545e-03 1.235381e-02 4.064651e-03 1.359729e-02 8.428279e-04
[9806] 4.912663e-03 6.752483e-03 3.282545e-02 5.657689e-03 2.162181e-04
[9811] 1.823218e-02 7.649649e-03 8.019317e-03 7.045173e-03 1.785134e-02
[9816] 1.529534e-02 2.800052e-03 1.850486e-03 2.308512e-03 7.868607e-03
[9821] 2.399104e-03 6.313553e-03 1.153505e-02 4.562985e-04 8.157842e-03
[9826] 7.325679e-03 4.759511e-03 4.870211e-03 1.027269e-02 9.072881e-03
[9831] 7.649649e-03 8.547827e-03 3.549755e-03 9.018037e-03 7.063047e-03
[9836] 2.283256e-02 5.170617e-03 1.617218e-02 1.704245e-03 1.149361e-02
[9841] 4.154022e-03 5.003047e-03 1.586385e-02 1.289796e-02 1.233269e-02
[9846] 2.328620e-03 8.227194e-04 1.526507e-02 9.365571e-03 2.231533e-03
[9851] 1.465177e-03 4.746105e-03 2.014148e-02 3.447992e-03 2.445363e-02
[9856] 3.402062e-05 8.257371e-03 3.678122e-03 1.998061e-02 7.020686e-04
[9861] 1.602249e-02 2.819148e-03 4.133914e-03 4.709254e-04 1.737869e-02
[9866] 1.032741e-03 1.676772e-02 1.088142e-02 9.837003e-03 9.815673e-03
[9871] 7.313286e-03 7.698803e-03 1.314474e-02 7.099027e-05 6.335895e-03
[9876] 9.904031e-03 4.581990e-03 8.631508e-03 4.504803e-03 2.564350e-04
[9881] 9.575593e-03 4.540552e-03 8.655072e-03 1.268471e-04 1.165448e-02
[9886] 7.703181e-04 1.141765e-02 5.178451e-04 9.547560e-03 1.306330e-02
[9891] 3.127477e-03 7.793655e-03 1.020557e-03 2.051907e-02 1.020891e-02
[9896] 2.546566e-03 6.352548e-03 5.558368e-03 1.791939e-02 5.771637e-03
[9901] 5.209821e-03 2.651577e-03 5.141572e-03 1.402850e-02 7.914396e-04
[9906] 4.767435e-03 2.193551e-03 6.921185e-04 4.250096e-03 1.108698e-02
[9911] 1.014086e-02 1.005251e-02 5.243335e-03 1.416479e-02 3.153067e-03
[9916] 9.415738e-03 4.037840e-03 6.729128e-03 5.500277e-03 7.857436e-03
[9921] 3.367558e-03 7.387017e-03 9.396851e-03 1.715326e-04 6.160401e-03
[9926] 1.496568e-02 5.817544e-03 4.307084e-04 3.304998e-03 2.054242e-02
[9931] 6.870900e-03 2.701744e-03 2.048779e-02 4.551723e-03 1.167459e-02
[9936] 1.179199e-02 4.444478e-03 1.573436e-03 1.582373e-03 1.629292e-03
[9941] 6.774916e-04 1.745475e-03 6.939149e-03 1.258516e-02 5.467776e-03
[9946] 1.301739e-02 5.367233e-03 2.846972e-03 1.188014e-02 6.782750e-03
[9951] 2.759156e-02 1.414346e-02 6.325737e-03 3.737434e-03 1.240418e-02
[9956] 1.210357e-02 4.418888e-03 2.965388e-03 1.287448e-03 8.317466e-05
[9961] 1.070491e-02 6.216257e-03 1.281854e-02 5.041029e-03 2.140485e-02
[9966] 6.010704e-03 2.734245e-03 2.855909e-03 6.591616e-03 6.790466e-03
[9971] 2.847857e-02 3.485974e-03 3.411230e-03 2.307499e-03 2.189762e-02
[9976] 4.207645e-03 1.268123e-02 4.672374e-03 3.177735e-04 5.930270e-03
[9981] 9.802268e-03 8.410315e-03 1.142110e-02 1.029279e-02 4.064651e-03
[9986] 1.585837e-02 7.017349e-03 4.942811e-04 1.609967e-02 5.256741e-03
[9991] 2.243718e-03 7.457501e-03 8.624805e-03 4.815368e-03 3.873725e-03
[9996] 1.505627e-02 2.254433e-02 1.590306e-02 6.220726e-03 1.753733e-02# Your code here
N <- 10^4
girlsAdiff <- numeric(N)
girlsWdiff <- numeric(N)
for(i in 1: N)
{
girlsAdiff[i] <- mean(sample(girlsA$Weight, length(girlsA$Weight), replace = FALSE))
girlsWdiff[i] <- mean(sample(girlsW$Weight, length(girlsW$Weight), replace = FALSE))
}
femaleDifference <- girlsAdiff - girlsWdiff
mean(femaleDifference)[1] 308.45- Not enough information to decide.
- Do chocolate and vanilla ice creams have the same number of calories? The data set
IceCreamcontains calorie information for a sample of brands of chocolate and vanilla ice cream. Use the bootstrap to determine whether or not there is a difference in the mean number of calories.
IceCream <- read.csv("http://www1.appstate.edu/~arnholta/Data/IceCream.csv")
head(IceCream) Brand VanillaCalories VanillaFat VanillaSugar ChocolateCalories
1 Baskin Robbins 260 16.0 26.0 260
2 Ben & Jerry's 240 16.0 19.0 260
3 Blue Bunny 140 7.0 12.0 130
4 Breyers 140 7.0 13.0 140
5 Brigham's 190 12.0 17.0 200
6 Bulla 234 13.5 21.8 266
ChocolateFat ChocolateSugar
1 14 31.0
2 16 22.0
3 7 14.0
4 8 16.0
5 12 18.0
6 15 22.6Your answer:
# Your code here
calChoc <- IceCream$ChocolateCalories
calVan <- IceCream$VanillaCalories
calDiff <- calVan - calChoc
meanDifference <- mean(calDiff)
simulation = 10^4
meanBootDifference <- numeric(simulation)
for(i in 1:simulation){
meanBootDifference[i] <- mean(sample(calDiff,length(calDiff),replace=TRUE))
}
quantile(meanBootDifference, prob = c(.05, .95)) 5% 95%
-10.717949 -4.025641 Based on the results from the confidence interval it is safe to say that there is a noticable difference in calorie content.
Import the data from Flight Delays Case Study in Section 1.1 data into
R. Although the data are on all UA and AA flights flown in May and June of 2009, we will assume these represent a sample from a larger population of UA and AA flights flown under similar circumstances. We will consider the ratio of the means of the flight delay lengths, \(\mu_{\text{UA}} / \mu_{\text{AA}}\).Perform some exploratory data analysis on flight delay lengths for each of UA and AA flights.
Bootstrap the mean of flight delay lengths for each airline seperately and describe the distribution.
Bootstrap the ratio of means. Provide plots of the bootstrap distribution and describe the distribution.
Find the 95% bootstrap percentile interval for the ratio of means. Interpret this interval.
What is the bootstrap estimate of the bias? What fraction of the bootstrap standard error does it represent?
For inference in this text, we assume that the observations are independent. Is that condition met here? Explain.
FlightDelays <- read.csv("http://www1.appstate.edu/~arnholta/Data/FlightDelays.csv")Your answers:
# Your code here
group_by(FlightDelays,Carrier) %>%
filter(Carrier =="UA") %>%
summarize(mean(Delay))# A tibble: 1 x 2
Carrier `mean(Delay)`
<fctr> <dbl>
1 UA 15.98308group_by(FlightDelays,Carrier) %>%
filter(Carrier =="AA") %>%
summarize(mean(Delay))# A tibble: 1 x 2
Carrier `mean(Delay)`
<fctr> <dbl>
1 AA 10.09738# Your code here
UA<-FlightDelays %>%
group_by(Carrier) %>%
filter(Carrier=="UA")
AA<-FlightDelays %>%
group_by(Carrier) %>%
filter(Carrier =="AA")
simulation<-10^4
UAMean<-numeric(simulation)
AAMean<-numeric(simulation)
for(i in 1:simulation)
{
UAMean[i]<-mean(sample(UA$Delay,length(UA$Delay),replace = TRUE))
AAMean[i]<-mean(sample(AA$Delay,length(AA$Delay),replace =TRUE))
}
hist(UAMean)
hist(AAMean)
The histograms have a normal distribution. c.
# Your code here
ratioMean<-numeric(simulation)
for(i in 1:simulation)
{
ratioMean[i]<-AAMean[i]/UAMean[i]
}
hist(ratioMean)
The distribution for this appears to be more left oriented than the previous histograms d.
# Your code here
quantile(ratioMean,c(.05,.95)) 5% 95%
0.5242160 0.7618419 # Your code here
difference <- AAMean - UAMean
oDifference <- mean(AA$Delay) - mean(UA$Delay)
oSd <- sd(AA$Delay) - sd(UA$Delay)
bDifference <- mean(difference)
bDifference[1] -5.884518bSD <- sd(difference)
bSD[1] 1.55063abs((bDifference - difference) / (sd(difference)*100)) [1] 6.459248e-03 4.595515e-03 9.005952e-03 8.315188e-03 1.500169e-02
[6] 8.533987e-03 2.945658e-03 2.768075e-03 1.253306e-02 1.239635e-02
[11] 7.522449e-03 7.372763e-03 9.298619e-03 1.629805e-02 2.981051e-03
[16] 3.573128e-03 1.792411e-03 6.312389e-03 1.893761e-02 1.150142e-03
[21] 8.863804e-03 3.656527e-03 1.897322e-02 1.165243e-02 5.156913e-03
[26] 1.231710e-02 9.178089e-03 2.372065e-03 2.294399e-03 7.312303e-03
[31] 2.340384e-02 2.296947e-03 3.057017e-03 1.192261e-02 9.718985e-04
[36] 5.287880e-03 1.838414e-03 7.215198e-03 4.938501e-03 4.948776e-04
[41] 1.575893e-02 1.882418e-03 3.798779e-03 2.492087e-02 7.770851e-03
[46] 7.641401e-03 9.247020e-03 7.784784e-04 6.990162e-03 2.409139e-02
[51] 3.305759e-03 1.221439e-03 7.225418e-03 6.348538e-03 5.560805e-04
[56] 1.577053e-02 6.233468e-03 8.519412e-04 9.598023e-03 9.749450e-03
[61] 2.761836e-03 4.073604e-03 2.882205e-03 1.119386e-03 1.739004e-02
[66] 1.185495e-02 3.114157e-03 1.606823e-02 4.113170e-03 6.809138e-03
[71] 6.102274e-03 1.814888e-03 1.327877e-02 7.229590e-03 3.076124e-03
[76] 3.595603e-03 8.074208e-03 2.442449e-03 1.208936e-02 1.341399e-02
[81] 1.347428e-02 1.087289e-03 9.167341e-03 6.402185e-03 9.663748e-03
[86] 2.524724e-03 5.028813e-03 1.576087e-04 5.533268e-03 3.175405e-03
[91] 3.313150e-03 1.296347e-02 6.515632e-03 2.521904e-03 9.851401e-03
[96] 1.283109e-02 2.678434e-02 3.043730e-03 1.166316e-02 1.544703e-02
[101] 1.053065e-03 1.653321e-03 2.260990e-02 6.156887e-03 9.462439e-03
[106] 2.565006e-02 9.546138e-03 1.264168e-02 2.064770e-02 2.681091e-03
[111] 2.114438e-02 1.244610e-02 6.836067e-03 1.893870e-03 6.125051e-04
[116] 7.493086e-03 9.992009e-03 3.783330e-03 5.700177e-03 8.598866e-03
[121] 2.934175e-03 3.838623e-04 5.771385e-03 1.336819e-02 1.676712e-02
[126] 4.748731e-03 9.067581e-03 1.081192e-02 2.002845e-02 5.535563e-03
[131] 4.126138e-03 1.304711e-03 6.945522e-04 1.664263e-02 1.526815e-02
[136] 1.119478e-02 1.069119e-02 4.016871e-03 1.019530e-02 6.587973e-03
[141] 1.017454e-02 2.210127e-03 7.912679e-03 5.784117e-03 1.469420e-02
[146] 1.101448e-02 1.787970e-02 1.490779e-02 1.154328e-02 5.174102e-03
[151] 1.262026e-02 7.189704e-03 7.350570e-04 2.646485e-03 1.014695e-02
[156] 2.619110e-03 9.989328e-03 2.743310e-03 1.048742e-02 6.307929e-03
[161] 1.488160e-02 1.779322e-02 4.737052e-03 2.539195e-03 2.829933e-02
[166] 1.302360e-03 3.039700e-03 1.813894e-03 3.799901e-03 7.180027e-03
[171] 6.744160e-03 1.734316e-02 1.725231e-02 4.460603e-03 6.867357e-03
[176] 7.491644e-04 4.563804e-03 3.414567e-03 1.031710e-03 3.095979e-03
[181] 2.498393e-03 6.597261e-03 1.715738e-02 1.673976e-02 1.901018e-02
[186] 1.008895e-02 9.264477e-03 5.682664e-03 1.180812e-02 1.022211e-02
[191] 1.037251e-02 7.745711e-03 4.114926e-04 8.019621e-03 3.938974e-03
[196] 1.509186e-03 7.214728e-04 4.093650e-03 4.062585e-03 4.694650e-03
[201] 3.366733e-03 6.301728e-03 3.108051e-03 5.401759e-03 9.150063e-03
[206] 1.282848e-02 9.145649e-04 8.310540e-03 1.671580e-02 1.036698e-03
[211] 1.827735e-03 1.683882e-03 7.092802e-03 4.709257e-03 3.919365e-03
[216] 2.638675e-04 1.396258e-02 3.792365e-03 8.075990e-03 2.766318e-03
[221] 6.393094e-04 3.979483e-03 1.052916e-02 1.795817e-02 3.494223e-03
[226] 1.469932e-02 8.197845e-03 1.095795e-02 1.243674e-02 9.440804e-03
[231] 6.733258e-03 1.055459e-03 6.858842e-03 2.740810e-03 9.304722e-03
[236] 1.786825e-02 4.986835e-03 1.013646e-02 2.270400e-02 1.107603e-02
[241] 2.180280e-02 4.245858e-03 1.444049e-02 1.014022e-02 9.770303e-03
[246] 3.872762e-03 2.035438e-02 8.391688e-03 1.011099e-03 1.421943e-02
[251] 1.902635e-03 8.030612e-03 5.456948e-03 7.066759e-03 7.867552e-03
[256] 9.959354e-03 1.360065e-03 1.909250e-03 1.909551e-03 1.063394e-02
[261] 5.313882e-03 6.457196e-03 4.779126e-03 5.048607e-03 1.126743e-02
[266] 1.078163e-02 4.005204e-03 2.581545e-03 2.198399e-03 9.919168e-04
[271] 1.111519e-02 6.005578e-03 1.097002e-02 6.933959e-03 3.507164e-04
[276] 2.843154e-03 2.225365e-02 4.044164e-03 5.304274e-03 1.214017e-02
[281] 4.439035e-03 1.368446e-02 3.787847e-03 3.002676e-03 3.485840e-03
[286] 8.344172e-03 4.495970e-03 3.339433e-03 4.605012e-03 9.711888e-03
[291] 3.312359e-03 2.397685e-04 1.328063e-02 1.017904e-02 2.295546e-02
[296] 5.022894e-03 1.327834e-02 6.429593e-03 9.557623e-03 1.765269e-03
[301] 3.010256e-03 1.195350e-03 1.423570e-03 1.104634e-02 2.661994e-03
[306] 1.724312e-03 2.398286e-02 4.780631e-03 9.603740e-03 2.686876e-02
[311] 1.119274e-02 1.457122e-02 1.239241e-02 1.137186e-02 3.836367e-03
[316] 3.127812e-03 1.374286e-02 1.161473e-03 9.359585e-03 2.297306e-03
[321] 1.736710e-02 1.557780e-02 7.964513e-04 1.066457e-03 8.879999e-03
[326] 1.522688e-02 1.670207e-03 2.963802e-02 8.160646e-03 5.027483e-04
[331] 5.444083e-03 5.865980e-03 7.305495e-04 1.446235e-02 4.086621e-03
[336] 1.813521e-03 6.259543e-03 7.200786e-03 4.917277e-04 1.807133e-02
[341] 4.087746e-03 4.269482e-03 2.023408e-02 7.681004e-03 1.209065e-03
[346] 1.848749e-02 1.406597e-02 2.650338e-02 1.043420e-02 1.194699e-02
[351] 1.415497e-02 6.388608e-03 1.264859e-03 1.158758e-03 9.726458e-03
[356] 4.955996e-03 1.147467e-02 2.262662e-02 9.926607e-03 4.223972e-03
[361] 6.734351e-03 1.084683e-02 1.323116e-02 1.313583e-02 1.310908e-02
[366] 1.011190e-02 1.105970e-02 4.059437e-04 3.988256e-04 5.292472e-03
[371] 2.467539e-04 2.710268e-02 2.431744e-02 5.155404e-03 1.095001e-02
[376] 1.781587e-02 3.474794e-03 9.478163e-03 3.195100e-02 4.258464e-03
[381] 1.950147e-02 1.720326e-02 1.589702e-02 1.013217e-02 9.605922e-03
[386] 8.642493e-03 6.838948e-03 9.790307e-03 1.116592e-02 1.160829e-02
[391] 3.536902e-03 1.731683e-02 1.135429e-02 3.041793e-03 6.233525e-03
[396] 6.328289e-03 1.918387e-02 1.160120e-03 1.159345e-02 1.094166e-02
[401] 1.038939e-02 4.158325e-03 3.758271e-03 1.932253e-02 1.087987e-02
[406] 6.878825e-04 2.183643e-03 1.068121e-02 2.920243e-03 6.505968e-04
[411] 1.573931e-02 4.891317e-03 3.724053e-03 1.482887e-02 2.230996e-04
[416] 5.738877e-03 9.195953e-03 5.181836e-03 5.671434e-03 8.260779e-03
[421] 1.805555e-02 1.108859e-03 1.111887e-02 2.477978e-02 1.865122e-03
[426] 5.894692e-03 2.356265e-04 3.576512e-03 2.070673e-02 5.136864e-03
[431] 4.237275e-03 6.694407e-03 5.284336e-03 2.093213e-02 6.786134e-03
[436] 1.185853e-02 8.673531e-04 1.800945e-02 9.253729e-03 3.111675e-02
[441] 1.716090e-02 9.534933e-03 5.024741e-03 1.957542e-02 6.470988e-03
[446] 2.059429e-03 1.985606e-03 9.294099e-04 5.672746e-03 6.052077e-03
[451] 5.432213e-03 5.765126e-03 3.021771e-03 5.758674e-03 4.454584e-04
[456] 6.698654e-03 3.606385e-03 1.702555e-03 1.630566e-02 1.454912e-02
[461] 2.329392e-03 6.111120e-03 7.534097e-03 6.425833e-03 1.226487e-02
[466] 1.020931e-02 2.141808e-02 1.275399e-02 4.753435e-04 1.935397e-02
[471] 1.101499e-02 4.016804e-03 7.841795e-03 2.299780e-03 1.069185e-02
[476] 5.307607e-03 3.251499e-03 1.712807e-03 3.901671e-03 5.149258e-03
[481] 8.602464e-03 5.238893e-03 6.341745e-03 5.413815e-03 1.437624e-02
[486] 1.239024e-05 1.081175e-02 8.452539e-03 8.847296e-03 6.529274e-03
[491] 8.088256e-03 1.732023e-02 1.110121e-02 4.862501e-03 1.619491e-02
[496] 1.737051e-02 1.663886e-02 1.191702e-02 7.809892e-03 1.162092e-03
[501] 2.444486e-03 6.489636e-03 1.039406e-02 1.411071e-02 2.770978e-03
[506] 1.351638e-02 8.505256e-03 1.101508e-02 1.666970e-03 3.037320e-04
[511] 2.713342e-03 2.775460e-03 3.354411e-04 4.655266e-03 2.672014e-02
[516] 1.143074e-02 1.664704e-03 1.336111e-02 1.319058e-02 1.566368e-02
[521] 3.940960e-03 3.936561e-03 1.490874e-02 6.225747e-03 6.953485e-03
[526] 4.725432e-03 7.800833e-03 1.319172e-02 6.185563e-03 2.912076e-03
[531] 1.771978e-03 8.367648e-03 9.557554e-03 5.506274e-03 4.067075e-03
[536] 9.134645e-04 4.067670e-03 5.545991e-03 1.527202e-02 1.161448e-02
[541] 3.464178e-03 8.174946e-03 2.157615e-02 1.646990e-03 1.192014e-02
[546] 3.055739e-03 5.178283e-03 1.499858e-02 3.640811e-03 8.631824e-03
[551] 8.764040e-04 4.887889e-04 7.610893e-03 7.515559e-03 1.082078e-02
[556] 7.434762e-03 5.547429e-03 1.599901e-02 8.432801e-04 1.223519e-02
[561] 2.354784e-02 4.845049e-04 1.042883e-02 5.568278e-03 4.279802e-03
[566] 2.918785e-03 1.467590e-02 1.645835e-02 2.916287e-03 6.933200e-03
[571] 7.824191e-03 1.085572e-02 1.075480e-02 7.218002e-03 1.213578e-02
[576] 3.739023e-03 6.714946e-03 5.393445e-03 1.641052e-03 2.589190e-04
[581] 1.959715e-03 4.994597e-03 1.457289e-02 7.054918e-03 1.881179e-02
[586] 1.006990e-02 2.029530e-03 4.134455e-03 3.982627e-03 3.543719e-03
[591] 1.784762e-02 9.787342e-04 3.844266e-03 5.772784e-03 2.534476e-02
[596] 1.664091e-03 1.755836e-02 3.489856e-03 6.822619e-03 2.699050e-03
[601] 6.167372e-03 1.409330e-03 7.167134e-03 3.420757e-03 1.509518e-02
[606] 8.932376e-03 2.187168e-03 1.926650e-02 6.504884e-03 1.306049e-03
[611] 1.708828e-02 2.446613e-03 1.377996e-02 2.296786e-03 1.553052e-03
[616] 2.797409e-02 1.470443e-02 2.142470e-03 1.197875e-02 6.268955e-03
[621] 2.022092e-02 1.922006e-02 7.282501e-03 9.291501e-03 8.308506e-03
[626] 5.707579e-03 3.728236e-04 3.307795e-03 5.216350e-03 1.290994e-02
[631] 2.247409e-02 1.404977e-02 1.438356e-02 9.445057e-03 8.076034e-03
[636] 4.782578e-03 9.208249e-03 1.654035e-03 5.597785e-03 1.236481e-02
[641] 1.169498e-02 1.585845e-02 7.935641e-03 1.839321e-03 1.845424e-02
[646] 1.080154e-02 1.582816e-02 1.801726e-02 2.730916e-03 2.506535e-03
[651] 2.836700e-03 1.981953e-02 8.487748e-03 6.530286e-03 4.041590e-04
[656] 1.624059e-02 1.310920e-03 1.991550e-02 3.168944e-03 1.005749e-02
[661] 8.352350e-04 8.473656e-03 2.232831e-03 2.967298e-02 2.656074e-02
[666] 1.260301e-02 2.435815e-03 2.934967e-03 8.326936e-03 1.779766e-02
[671] 2.983845e-03 2.294427e-03 4.898899e-04 1.312970e-03 3.522461e-04
[676] 7.589622e-03 9.752227e-03 2.598611e-03 3.222182e-03 6.726307e-04
[681] 1.376151e-02 1.839258e-02 2.772228e-03 5.143069e-03 2.860918e-03
[686] 1.166250e-02 3.494767e-03 5.975276e-03 1.712501e-02 2.418139e-02
[691] 8.218049e-03 1.426358e-02 1.502062e-03 8.516038e-03 4.987311e-04
[696] 9.081434e-03 1.933026e-02 5.089381e-03 5.392320e-04 1.894446e-02
[701] 2.806246e-03 6.867007e-03 9.753342e-03 3.668176e-03 1.114126e-02
[706] 1.657627e-03 1.833588e-03 6.258844e-03 4.625612e-03 1.987913e-02
[711] 7.269358e-03 1.408494e-02 9.387211e-03 8.006413e-03 5.660172e-03
[716] 1.380082e-02 1.214213e-02 2.819745e-03 3.064139e-03 6.236386e-04
[721] 7.490490e-03 1.768341e-02 1.474001e-03 1.296505e-03 4.383134e-03
[726] 1.995734e-02 8.310694e-03 6.547743e-03 1.738505e-03 1.991241e-02
[731] 1.403731e-03 7.913906e-03 1.428138e-02 9.676577e-04 1.014506e-02
[736] 2.124804e-02 1.826761e-03 2.040259e-02 1.166903e-02 1.966298e-02
[741] 1.237992e-02 9.989792e-03 5.904376e-03 5.442277e-03 4.865793e-03
[746] 1.336088e-02 1.155016e-02 7.343894e-03 8.708451e-03 1.245060e-02
[751] 8.947367e-03 5.936226e-03 8.214594e-03 4.272738e-04 1.165684e-03
[756] 1.955456e-03 3.186648e-03 1.607141e-03 1.739643e-02 4.042233e-03
[761] 1.319505e-02 1.222863e-02 2.202520e-04 1.154497e-02 4.764248e-03
[766] 1.743753e-02 1.010852e-02 3.880686e-03 2.912184e-03 1.393158e-02
[771] 8.549279e-03 3.706539e-03 1.000736e-03 1.121880e-02 4.269556e-03
[776] 2.450206e-03 1.806474e-03 8.796474e-03 2.302439e-02 1.762516e-03
[781] 1.307092e-02 1.975739e-02 1.017494e-02 7.302587e-04 1.185956e-02
[786] 3.534527e-05 1.043412e-02 1.011477e-03 2.820770e-03 3.014957e-03
[791] 1.067466e-02 4.309527e-03 2.591974e-02 7.908479e-05 1.324071e-02
[796] 1.577599e-02 1.127522e-02 1.286185e-03 4.572325e-03 2.024252e-02
[801] 1.075798e-03 1.147138e-02 8.127186e-03 6.379625e-03 3.603926e-03
[806] 9.554481e-03 3.244667e-03 1.115916e-02 5.510306e-03 1.474909e-04
[811] 6.771566e-03 4.468454e-03 3.317808e-03 9.808997e-03 1.724545e-02
[816] 4.511595e-03 1.091969e-02 8.022969e-03 2.147401e-03 5.286665e-03
[821] 1.098493e-04 7.907041e-03 1.482945e-02 1.554825e-02 8.221138e-03
[826] 7.145369e-04 1.291346e-02 1.949887e-02 1.510269e-03 1.600136e-03
[831] 8.126103e-03 2.772167e-03 7.742241e-03 8.787359e-03 5.191740e-04
[836] 3.835879e-03 1.206086e-03 1.320000e-02 1.780885e-03 1.972863e-02
[841] 1.873044e-03 2.893672e-03 3.269776e-03 7.942074e-03 5.359509e-03
[846] 3.101069e-03 7.971077e-04 3.134600e-03 1.684911e-02 4.540717e-03
[851] 2.030773e-03 1.614895e-02 1.039994e-02 1.177144e-02 8.582130e-03
[856] 7.584308e-04 1.189381e-02 1.523542e-02 3.509649e-03 2.156579e-02
[861] 6.005356e-04 1.873303e-03 9.489449e-03 1.164354e-02 2.080686e-03
[866] 2.575995e-02 1.367162e-02 6.359069e-03 1.331353e-02 5.946814e-03
[871] 7.767178e-03 1.225789e-02 1.906317e-02 1.978109e-03 1.197243e-03
[876] 1.638941e-03 2.094859e-03 4.940045e-03 1.562892e-02 3.122597e-03
[881] 3.557414e-03 3.257820e-03 5.105417e-03 5.242079e-03 4.746161e-04
[886] 8.580181e-04 1.125274e-02 4.554801e-03 5.325323e-03 1.889029e-03
[891] 1.595788e-02 7.619680e-04 9.929099e-03 2.812374e-03 1.820061e-03
[896] 1.747739e-03 1.895909e-03 1.911168e-02 3.478147e-03 1.600133e-02
[901] 9.489812e-03 8.574765e-03 5.268284e-03 7.721452e-03 9.596339e-03
[906] 6.624110e-03 1.786363e-02 1.105772e-02 8.796541e-03 2.775744e-03
[911] 6.613384e-03 7.226059e-03 2.679937e-03 8.373793e-04 6.781314e-03
[916] 7.453719e-03 7.869625e-03 2.548281e-02 3.072058e-04 3.632668e-04
[921] 1.530977e-02 1.413320e-03 1.048619e-02 1.905155e-02 1.118639e-02
[926] 6.557501e-03 5.441702e-03 7.962004e-04 1.693022e-02 1.136429e-02
[931] 1.834525e-02 3.467901e-03 1.437810e-03 2.144668e-03 1.371672e-02
[936] 2.171221e-02 2.120973e-05 2.764140e-03 1.040238e-02 5.942565e-03
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[1851] 9.812891e-04 1.118968e-02 3.390755e-03 1.071025e-02 6.670820e-03
[1856] 2.934464e-02 1.289670e-02 1.247771e-02 1.337891e-02 2.393506e-02
[1861] 6.516733e-03 1.415955e-02 3.809091e-03 4.396475e-03 1.563882e-02
[1866] 1.454002e-02 8.318174e-03 1.621673e-02 1.727057e-02 1.090906e-02
[1871] 4.367558e-03 1.365338e-02 1.143286e-02 4.418562e-03 9.126707e-03
[1876] 1.367418e-02 6.223915e-03 2.008041e-02 1.447565e-02 2.773019e-03
[1881] 1.451292e-02 4.183776e-03 3.632353e-03 1.296825e-02 1.797206e-02
[1886] 2.144114e-03 8.837939e-03 2.542389e-02 9.861061e-03 1.481471e-02
[1891] 1.634092e-02 5.089754e-03 1.694895e-02 8.659824e-03 1.105463e-02
[1896] 7.830460e-03 5.058647e-04 6.670231e-03 2.243959e-04 9.164603e-03
[1901] 4.268238e-03 7.301551e-03 6.687604e-03 8.842691e-03 1.208096e-02
[1906] 3.730563e-03 8.821381e-03 1.737355e-02 2.069839e-02 2.160411e-03
[1911] 7.663735e-03 9.409367e-04 1.029398e-02 2.576736e-03 1.987628e-03
[1916] 1.651426e-02 6.147137e-03 6.025290e-03 9.260410e-03 2.798392e-02
[1921] 1.694996e-02 7.481399e-03 7.039180e-03 7.855802e-03 3.947580e-03
[1926] 1.564902e-02 9.532281e-03 1.888823e-03 6.744153e-03 2.506511e-04
[1931] 2.917868e-03 9.113716e-03 1.026276e-03 1.936039e-02 4.254428e-03
[1936] 8.173458e-03 2.697466e-03 2.622495e-03 4.312126e-03 5.392147e-03
[1941] 3.519356e-03 1.533036e-02 1.054427e-02 6.176263e-03 6.450873e-04
[1946] 1.133354e-02 8.792333e-03 4.104418e-03 1.575644e-02 8.249096e-03
[1951] 5.664545e-03 5.410133e-03 1.052267e-02 1.964576e-02 1.632576e-02
[1956] 1.731310e-02 5.187435e-03 2.234558e-03 2.748025e-03 1.429028e-03
[1961] 1.250823e-02 7.478988e-03 6.046585e-03 6.929727e-03 3.379224e-03
[1966] 8.581970e-03 1.339683e-02 1.326779e-03 1.756716e-02 9.577968e-04
[1971] 3.414187e-04 5.418012e-03 5.984890e-03 6.368124e-03 1.532366e-03
[1976] 1.390025e-03 7.004244e-03 1.497500e-02 1.999882e-03 1.032181e-02
[1981] 9.571535e-03 3.359797e-03 2.626856e-03 1.676770e-02 2.994336e-03
[1986] 7.568736e-03 5.168756e-03 4.547582e-03 4.012866e-03 9.265640e-03
[1991] 2.095265e-02 5.398166e-03 5.821181e-03 3.469800e-03 1.129153e-02
[1996] 4.830948e-03 6.671733e-03 1.579228e-02 1.486121e-03 2.452954e-02
[2001] 1.004171e-03 7.448799e-03 3.141781e-03 1.476521e-02 1.794336e-03
[2006] 4.368807e-03 8.467208e-03 7.805124e-03 1.325291e-03 3.694015e-03
[2011] 1.638931e-03 4.360439e-04 3.078765e-03 1.089489e-02 9.866317e-03
[2016] 1.461802e-03 1.732582e-02 6.479479e-03 9.065064e-03 4.509146e-03
[2021] 8.348679e-03 3.676259e-03 7.061192e-03 6.681234e-03 2.089225e-03
[2026] 7.355392e-04 9.280196e-03 3.800194e-03 8.126014e-03 1.110066e-02
[2031] 2.184228e-03 5.077099e-03 1.384426e-02 1.547388e-03 1.219972e-02
[2036] 1.037016e-02 9.571920e-03 1.508187e-02 2.561293e-02 1.361537e-03
[2041] 2.453838e-02 9.928480e-03 1.369002e-02 1.729514e-02 1.110156e-02
[2046] 8.433847e-03 5.353164e-05 9.900933e-03 2.477727e-03 2.010353e-03
[2051] 5.542797e-03 3.801957e-03 4.743982e-03 1.116572e-02 9.615840e-03
[2056] 1.550599e-02 5.114616e-03 9.130468e-03 8.090021e-03 1.770862e-02
[2061] 1.116435e-02 5.657929e-03 1.549268e-02 9.602426e-03 9.053821e-04
[2066] 1.432144e-02 6.703684e-03 6.766216e-03 7.792986e-03 2.273363e-03
[2071] 8.097983e-03 2.253773e-02 2.324425e-03 7.509168e-03 2.636995e-04
[2076] 3.722277e-03 1.581497e-02 3.959809e-03 4.419724e-03 1.592636e-03
[2081] 5.028038e-03 2.875495e-03 1.476636e-02 1.422549e-02 8.649581e-03
[2086] 1.786915e-02 1.052584e-03 4.418926e-03 6.452090e-03 1.367925e-02
[2091] 1.815713e-02 2.964141e-03 2.059460e-02 2.300535e-03 1.528608e-02
[2096] 2.754689e-02 3.056118e-03 5.442683e-05 5.236564e-03 1.537015e-02
[2101] 9.750851e-03 1.778379e-03 3.925475e-03 1.069449e-02 2.770094e-03
[2106] 1.163485e-02 2.456325e-02 4.295518e-03 1.584778e-02 1.054627e-02
[2111] 2.972419e-03 1.529420e-02 1.060757e-02 1.320375e-02 1.314460e-02
[2116] 6.067791e-03 2.288318e-03 1.536275e-02 1.506334e-02 3.255233e-03
[2121] 1.258880e-02 6.509242e-03 8.598607e-03 2.364266e-04 1.760748e-03
[2126] 3.376977e-03 1.179766e-02 5.662249e-03 7.316993e-04 5.990828e-03
[2131] 1.467547e-03 2.842648e-03 6.245414e-03 4.264181e-04 1.369502e-02
[2136] 1.251827e-02 6.290497e-03 7.124588e-03 5.063928e-03 1.409645e-02
[2141] 1.247964e-02 9.101269e-03 1.867711e-02 2.925800e-03 7.131343e-03
[2146] 1.735081e-02 1.354365e-02 2.357379e-03 8.293017e-03 1.533477e-03
[2151] 1.445937e-02 1.089795e-03 5.482242e-03 1.534651e-02 1.547018e-02
[2156] 5.437916e-03 8.002450e-03 1.856978e-03 8.631936e-04 1.944286e-03
[2161] 1.357125e-02 4.321035e-04 1.226849e-02 5.223292e-03 6.794301e-03
[2166] 7.808359e-03 8.971015e-03 1.365845e-02 2.701563e-02 6.201645e-03
[2171] 1.725740e-04 2.508509e-02 1.404024e-03 2.675908e-03 4.521888e-03
[2176] 8.811686e-03 1.132013e-03 2.418709e-02 1.636640e-02 7.057095e-03
[2181] 5.336941e-03 1.236466e-02 1.000905e-02 1.029381e-02 6.932925e-03
[2186] 3.568032e-03 1.237594e-02 2.143529e-02 1.175099e-02 1.992846e-02
[2191] 9.042943e-03 5.734553e-03 3.061744e-03 1.357640e-03 1.988713e-03
[2196] 1.697543e-02 7.566487e-03 2.978321e-03 1.278772e-02 5.374673e-03
[2201] 1.654996e-02 6.676013e-03 5.919636e-03 8.284356e-03 8.746199e-03
[2206] 6.986563e-03 6.576952e-03 9.822495e-03 5.155342e-03 1.286176e-02
[2211] 1.832097e-02 7.965479e-03 4.282762e-03 1.111631e-02 2.089622e-03
[2216] 2.171948e-02 6.413579e-03 8.272229e-03 3.163786e-03 1.371640e-02
[2221] 2.131130e-02 6.627407e-03 7.983820e-04 7.201807e-04 1.835782e-03
[2226] 8.543024e-03 2.590264e-03 1.880541e-02 1.309014e-02 4.273354e-03
[2231] 1.272252e-02 1.303615e-03 1.637489e-02 9.416067e-03 9.675187e-03
[2236] 4.161196e-03 2.067747e-04 1.388649e-02 2.869230e-04 3.415152e-02
[2241] 2.948051e-03 8.131312e-03 1.802348e-02 3.843321e-03 1.981893e-02
[2246] 1.334643e-02 2.798316e-03 1.866903e-02 3.363842e-03 5.677993e-03
[2251] 5.546636e-04 1.017695e-02 1.373406e-03 1.760339e-03 6.893537e-03
[2256] 6.347048e-03 2.480478e-03 1.250219e-02 1.475649e-03 9.388254e-03
[2261] 4.827950e-03 9.015236e-03 7.136103e-03 2.011172e-02 5.878778e-03
[2266] 1.658471e-02 5.116707e-03 2.996937e-03 1.593701e-02 8.209951e-03
[2271] 4.608654e-03 1.164633e-02 7.398340e-03 2.075951e-03 1.241300e-02
[2276] 1.860877e-03 1.612546e-02 4.295987e-03 5.850968e-03 1.202696e-02
[2281] 1.415494e-02 3.377254e-03 9.504878e-03 1.429838e-03 2.050698e-03
[2286] 2.125937e-02 1.454929e-02 9.260426e-04 1.529463e-02 6.705837e-04
[2291] 2.586456e-03 7.968532e-03 9.185984e-03 1.263027e-02 6.473181e-03
[2296] 1.640372e-03 9.350645e-03 1.180995e-02 5.798104e-03 4.121267e-03
[2301] 6.033161e-03 7.528749e-03 1.546736e-02 8.638143e-03 2.150641e-02
[2306] 1.607812e-02 2.267939e-03 2.363169e-03 7.368252e-03 1.025041e-02
[2311] 2.504485e-02 4.566494e-03 1.532925e-02 8.421344e-03 1.231295e-02
[2316] 5.349118e-03 1.160093e-02 7.764929e-03 1.547049e-02 5.936931e-03
[2321] 1.502125e-02 8.073983e-03 7.295455e-03 1.225456e-02 7.292631e-03
[2326] 1.445268e-02 1.151641e-02 3.367041e-03 2.144468e-02 8.095317e-03
[2331] 6.709418e-03 1.403002e-02 5.683486e-03 9.751749e-03 2.395669e-02
[2336] 2.324838e-02 1.275746e-02 9.652511e-04 1.561177e-02 1.488626e-02
[2341] 4.009423e-03 8.419763e-03 1.261925e-02 4.744049e-03 1.220153e-02
[2346] 1.157234e-02 8.009590e-03 3.117371e-04 1.496057e-02 3.662844e-04
[2351] 1.563002e-02 1.197514e-02 6.908644e-03 1.386269e-02 1.095755e-02
[2356] 7.822205e-03 1.456927e-02 3.655531e-03 3.368622e-03 4.872716e-03
[2361] 1.322426e-02 1.038716e-03 1.353725e-02 1.216275e-02 2.586405e-03
[2366] 8.527626e-03 2.860869e-04 8.739527e-03 2.765780e-03 1.446702e-02
[2371] 1.078057e-02 1.921306e-02 9.151573e-03 9.454987e-03 1.839754e-02
[2376] 1.972388e-02 7.285756e-03 2.179928e-03 5.222622e-03 3.199005e-04
[2381] 2.264785e-03 8.970462e-03 2.801558e-03 1.143431e-03 2.167484e-03
[2386] 7.300258e-04 1.295104e-02 3.192161e-03 7.599973e-03 1.292766e-02
[2391] 4.293548e-03 9.899352e-03 1.762820e-02 5.591368e-03 1.636413e-03
[2396] 7.232219e-03 1.109380e-03 9.373552e-03 9.432998e-03 2.993196e-03
[2401] 2.356452e-03 4.994722e-03 6.412598e-04 1.125198e-02 9.049205e-03
[2406] 1.052673e-02 8.064434e-03 1.045260e-02 3.913835e-04 2.876436e-03
[2411] 4.376056e-03 4.266617e-03 4.612599e-03 1.719155e-02 1.079938e-02
[2416] 4.090844e-03 1.368102e-02 2.142768e-03 1.813966e-02 1.071774e-02
[2421] 4.435224e-05 1.064568e-02 3.572020e-03 1.546464e-02 3.277850e-03
[2426] 5.309613e-03 1.592427e-02 2.060152e-02 9.361253e-03 1.120413e-03
[2431] 8.197378e-03 1.459250e-02 1.305516e-02 1.845218e-02 3.475082e-03
[2436] 1.241835e-03 1.102757e-02 5.421306e-03 3.845094e-03 1.174755e-02
[2441] 4.482556e-03 6.050014e-03 9.381797e-04 3.704834e-03 4.541519e-03
[2446] 2.093721e-03 2.366980e-02 4.723164e-03 1.908178e-02 1.111030e-03
[2451] 2.949885e-03 1.593686e-02 2.114982e-02 1.590750e-02 3.682654e-03
[2456] 1.633005e-03 9.251672e-03 6.873042e-03 7.743482e-03 8.329264e-03
[2461] 3.508829e-03 1.580701e-02 2.745252e-03 5.291534e-04 6.290343e-03
[2466] 1.371946e-02 1.650424e-03 1.615517e-02 1.283033e-02 5.293684e-03
[2471] 1.668585e-03 1.908602e-02 6.007657e-03 7.932740e-04 9.241924e-03
[2476] 1.373328e-02 1.013441e-02 1.288720e-02 4.454767e-03 2.073866e-03
[2481] 1.116608e-02 2.311803e-03 1.164086e-02 1.097459e-02 1.459123e-03
[2486] 4.252672e-03 4.775488e-03 1.279402e-02 1.302213e-03 8.568362e-03
[2491] 1.071215e-03 4.485024e-03 2.124633e-02 7.163075e-03 4.284282e-03
[2496] 1.094098e-02 1.016125e-02 4.938391e-03 7.064618e-03 4.232645e-04
[2501] 6.216185e-03 1.483352e-03 5.665651e-03 5.381090e-03 3.001630e-03
[2506] 1.704790e-02 7.769727e-03 1.224763e-03 3.591682e-03 8.944165e-04
[2511] 7.915437e-03 8.285484e-03 5.961918e-03 1.486665e-02 6.388502e-03
[2516] 3.226899e-03 2.687551e-03 9.314738e-03 1.753102e-02 4.464770e-03
[2521] 2.120960e-03 9.140606e-03 1.109750e-02 5.813807e-04 1.353324e-03
[2526] 2.182245e-03 1.165985e-02 1.045505e-02 1.473279e-02 2.598453e-03
[2531] 1.345091e-02 1.495078e-02 7.061304e-04 3.214624e-03 3.154775e-03
[2536] 6.038623e-03 7.281782e-03 1.577535e-02 6.887219e-03 9.432349e-04
[2541] 2.163684e-03 7.358845e-03 2.822774e-03 4.984050e-04 4.655984e-05
[2546] 2.460948e-03 5.741950e-03 2.601526e-03 2.822859e-03 3.517633e-03
[2551] 3.666691e-03 6.142900e-03 2.098629e-02 2.972312e-03 4.206778e-03
[2556] 8.204799e-03 3.149888e-03 6.077494e-03 5.748991e-03 3.935077e-03
[2561] 1.670841e-02 7.244336e-03 1.907996e-03 1.909259e-02 5.813669e-04
[2566] 4.540053e-03 1.198277e-03 1.046142e-02 1.117337e-02 4.396566e-03
[2571] 2.613543e-03 6.051634e-03 8.143161e-03 1.482127e-02 4.797806e-03
[2576] 1.226530e-02 6.410916e-04 1.008435e-03 1.334754e-02 1.310099e-02
[2581] 1.306697e-03 1.962150e-03 2.162504e-02 1.072436e-03 2.529551e-03
[2586] 3.817272e-03 8.495988e-03 5.550113e-03 6.618510e-03 3.108298e-03
[2591] 3.065801e-03 9.869507e-04 3.050573e-03 1.697508e-02 1.348012e-02
[2596] 5.255412e-03 2.323843e-02 6.063808e-04 4.192433e-03 2.836233e-03
[2601] 1.028182e-02 1.571101e-02 1.884829e-02 5.396352e-03 1.670503e-02
[2606] 1.146176e-02 5.710097e-03 1.702297e-02 6.087586e-03 1.120413e-02
[2611] 5.940524e-03 1.538315e-02 4.970329e-03 1.466978e-03 5.653072e-03
[2616] 6.823726e-03 5.436993e-03 3.863267e-03 6.862598e-03 2.315500e-03
[2621] 3.987139e-03 1.720308e-03 4.379686e-04 1.230214e-02 2.526716e-03
[2626] 1.576896e-02 1.438748e-02 6.013732e-03 1.059993e-02 8.766887e-03
[2631] 7.497661e-03 2.082581e-02 1.261820e-02 1.631926e-03 4.951041e-03
[2636] 1.786695e-03 7.806343e-03 2.866998e-03 1.340046e-02 6.284229e-03
[2641] 1.271073e-02 3.030533e-03 3.268997e-03 1.821307e-02 2.172802e-03
[2646] 3.274210e-03 2.217443e-02 2.262890e-03 3.019376e-03 1.876923e-03
[2651] 1.103117e-02 1.445208e-04 4.534737e-03 1.029477e-02 6.273712e-03
[2656] 1.044183e-02 3.699496e-03 8.522502e-03 6.853490e-03 3.031960e-03
[2661] 3.915782e-03 2.153542e-03 1.949870e-03 8.531296e-03 9.099600e-03
[2666] 9.646340e-03 5.422439e-03 1.057524e-03 7.604688e-03 1.256400e-02
[2671] 1.303097e-02 3.573316e-03 7.231827e-03 1.295163e-02 6.159217e-03
[2676] 5.191545e-03 6.612362e-03 1.059000e-02 4.481895e-03 2.245523e-04
[2681] 3.166295e-03 9.133288e-03 4.015083e-03 6.067718e-03 1.284161e-03
[2686] 5.523219e-03 1.938308e-03 7.676072e-03 1.329046e-02 1.065178e-02
[2691] 7.260228e-03 2.072835e-03 9.760495e-03 2.013914e-02 5.757445e-03
[2696] 5.742626e-03 1.511059e-03 5.105800e-04 6.678484e-03 3.665054e-03
[2701] 7.390052e-03 3.535252e-03 9.667749e-03 1.539463e-02 2.865032e-03
[2706] 1.876757e-03 1.065750e-02 1.721937e-02 1.283079e-02 2.091199e-03
[2711] 3.383295e-03 1.195332e-02 9.085781e-03 8.479986e-03 6.394361e-03
[2716] 4.369196e-04 9.353850e-03 1.163117e-02 2.994822e-03 1.494351e-02
[2721] 5.815753e-03 8.490287e-03 6.729120e-03 5.913943e-03 1.002326e-02
[2726] 2.013661e-02 2.206859e-02 9.844779e-03 2.196871e-03 1.331924e-02
[2731] 8.661616e-03 4.711258e-03 3.644279e-03 8.350114e-03 4.857798e-03
[2736] 1.227947e-02 5.409827e-03 9.434257e-03 2.331365e-03 3.824374e-03
[2741] 1.708173e-03 7.784184e-03 2.696414e-03 1.526083e-02 3.122421e-03
[2746] 3.441998e-03 1.139354e-03 9.011726e-03 1.861962e-03 6.482465e-03
[2751] 1.445191e-03 4.598511e-03 2.741626e-02 3.296705e-03 4.479115e-03
[2756] 1.774719e-02 1.215370e-03 3.483097e-03 8.924630e-03 1.762748e-02
[2761] 5.095339e-03 5.121035e-03 4.333134e-03 1.270834e-02 7.686848e-03
[2766] 1.566914e-02 5.754918e-04 1.341118e-03 2.416076e-03 2.441198e-03
[2771] 1.023639e-02 1.053008e-02 8.345116e-03 2.117425e-02 1.364395e-03
[2776] 8.304738e-03 8.521664e-03 2.992998e-03 1.122853e-02 7.820958e-03
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[9191] 2.603425e-02 1.028729e-02 7.770800e-03 3.974539e-03 6.080130e-03
[9196] 2.443334e-03 5.207639e-03 1.613848e-02 3.675322e-03 1.423561e-02
[9201] 2.396358e-02 8.488210e-03 8.002014e-03 1.616308e-03 2.873338e-04
[9206] 4.085699e-04 6.591105e-03 9.008455e-03 2.475344e-02 8.905693e-03
[9211] 1.178120e-03 6.851026e-03 2.808767e-03 1.178116e-02 3.760596e-03
[9216] 3.353107e-04 3.261858e-03 1.087769e-03 5.871442e-03 1.299310e-02
[9221] 2.632318e-03 1.332803e-04 1.130725e-02 1.688364e-02 1.607153e-03
[9226] 7.073793e-04 7.302212e-04 2.679208e-03 5.265729e-03 1.498976e-02
[9231] 2.585695e-04 3.542127e-03 3.135100e-03 1.203157e-02 8.642714e-03
[9236] 4.520807e-03 3.583975e-03 1.293672e-02 5.054134e-03 5.701016e-03
[9241] 1.266472e-02 1.282876e-02 3.661086e-03 2.868120e-03 1.318565e-02
[9246] 1.809341e-02 3.250412e-03 2.261639e-03 1.892616e-02 2.267006e-03
[9251] 5.344834e-03 1.652496e-02 1.677580e-03 4.839263e-03 6.982970e-03
[9256] 5.455912e-04 3.920556e-03 9.055854e-04 5.281854e-03 9.551551e-03
[9261] 2.681490e-03 1.002633e-02 1.025452e-03 9.531643e-03 1.952065e-03
[9266] 1.775884e-02 6.504541e-03 4.219125e-03 2.678295e-03 3.714709e-03
[9271] 8.190622e-03 1.147146e-03 2.706475e-03 1.770308e-02 4.355261e-03
[9276] 7.438684e-04 1.648987e-02 2.502600e-02 2.542023e-03 7.678009e-03
[9281] 1.653411e-02 3.269444e-03 3.353007e-03 1.294878e-03 9.991021e-03
[9286] 2.455670e-02 4.081805e-03 8.002848e-03 3.468302e-03 3.747323e-04
[9291] 2.047568e-03 9.581357e-03 1.283019e-02 1.074565e-02 5.773296e-03
[9296] 1.339856e-02 4.815301e-03 1.283938e-02 8.399053e-03 5.029312e-03
[9301] 2.795348e-02 4.980107e-03 1.166685e-02 2.829194e-04 2.874570e-03
[9306] 1.513858e-02 9.986061e-03 2.192523e-04 3.336907e-03 1.410258e-02
[9311] 1.292610e-02 2.096256e-02 4.229877e-03 6.231521e-03 1.989092e-03
[9316] 1.258551e-03 1.322114e-02 4.340564e-03 1.221184e-02 4.290076e-03
[9321] 3.086660e-02 8.577954e-03 1.788512e-02 5.424429e-04 5.535598e-03
[9326] 2.643594e-03 3.965622e-03 1.499269e-02 2.655613e-03 1.106745e-02
[9331] 1.296325e-02 1.347637e-03 2.792638e-03 6.528219e-04 7.071676e-04
[9336] 7.078697e-03 8.268621e-04 5.623651e-03 5.281855e-03 3.344197e-03
[9341] 1.104409e-02 2.859242e-03 1.074876e-02 1.998781e-03 6.412201e-03
[9346] 1.159753e-02 2.924152e-03 1.128365e-02 4.763973e-03 1.121173e-02
[9351] 2.435527e-03 1.463025e-02 1.793774e-02 7.409731e-03 1.012748e-02
[9356] 5.998559e-03 5.978646e-03 1.561100e-02 7.752830e-04 1.433428e-02
[9361] 1.313252e-02 1.763973e-03 2.222178e-02 4.595045e-03 8.572524e-03
[9366] 9.638706e-03 5.974407e-04 2.222541e-02 7.477647e-03 2.673477e-03
[9371] 1.274147e-02 4.276984e-03 3.689078e-03 1.708704e-02 1.586457e-03
[9376] 1.161828e-02 2.729186e-03 2.223310e-03 7.665555e-03 5.655222e-04
[9381] 1.220964e-02 1.371399e-04 8.767219e-04 4.114587e-03 3.796048e-03
[9386] 2.810486e-03 1.760243e-02 1.072909e-03 2.470265e-03 4.224735e-03
[9391] 6.789602e-03 2.435574e-03 7.377356e-03 1.831353e-03 6.442554e-04
[9396] 3.224661e-03 3.042084e-03 1.126051e-02 1.963262e-02 1.368390e-02
[9401] 7.855663e-03 8.565333e-03 5.085598e-03 4.429516e-03 3.947054e-04
[9406] 2.396855e-04 2.803205e-04 1.699529e-02 1.507786e-02 1.845006e-02
[9411] 9.936938e-03 1.014538e-03 9.325181e-04 1.182551e-02 2.568359e-03
[9416] 6.168361e-03 1.143464e-02 1.061679e-02 8.969221e-03 4.201340e-03
[9421] 7.673057e-03 7.082683e-04 9.758511e-03 6.728634e-03 2.045077e-02
[9426] 2.212062e-03 2.562989e-02 1.524268e-02 6.501673e-03 2.712838e-03
[9431] 7.940016e-03 5.779212e-03 6.778526e-03 1.012843e-02 1.672797e-04
[9436] 3.274949e-03 2.018045e-03 5.132382e-03 1.083756e-02 8.138000e-03
[9441] 1.229623e-02 1.722498e-02 3.462841e-04 8.240303e-04 6.727889e-03
[9446] 2.988038e-03 1.102663e-02 9.222599e-03 1.621436e-02 3.111264e-03
[9451] 7.119841e-03 7.573341e-03 6.635120e-03 2.413511e-03 4.360519e-03
[9456] 1.422280e-02 7.388531e-03 3.491089e-03 8.622544e-03 1.516869e-02
[9461] 9.199016e-03 4.148847e-03 1.083285e-02 2.468981e-03 1.160888e-02
[9466] 3.108486e-03 1.679163e-02 2.361392e-03 1.508845e-02 1.929925e-03
[9471] 4.724699e-03 2.675175e-03 4.279255e-03 1.250980e-02 1.177624e-02
[9476] 8.805340e-03 1.421984e-02 3.001081e-03 5.369779e-03 1.788651e-03
[9481] 1.248066e-02 1.309255e-02 1.241181e-02 6.144858e-03 1.148937e-03
[9486] 1.453936e-02 1.417763e-02 2.481947e-04 2.933028e-03 1.241491e-02
[9491] 1.162715e-02 4.697831e-03 1.663285e-02 7.602965e-03 9.672905e-03
[9496] 6.537297e-03 1.360253e-02 2.799343e-03 5.380649e-03 3.507208e-03
[9501] 1.544479e-02 2.296980e-03 2.437329e-03 1.984990e-02 1.649673e-02
[9506] 2.503399e-03 6.942126e-03 9.324076e-03 7.176085e-03 9.520484e-03
[9511] 3.909247e-03 1.141444e-02 5.656257e-03 8.649105e-03 8.051890e-03
[9516] 1.367778e-02 1.418271e-02 2.648291e-02 5.155087e-03 7.682632e-05
[9521] 3.660808e-03 8.219534e-04 2.679503e-03 6.676274e-04 9.443839e-03
[9526] 5.917502e-03 1.757139e-03 1.048344e-02 9.073192e-03 7.297528e-03
[9531] 2.271923e-02 9.930686e-03 9.308948e-03 1.019923e-02 1.199378e-02
[9536] 7.391655e-03 3.935806e-03 3.002950e-03 6.840053e-03 1.557087e-02
[9541] 1.188031e-02 2.635454e-02 1.245321e-02 2.385881e-02 2.180997e-03
[9546] 1.091842e-02 6.207561e-03 1.292113e-02 5.913207e-04 9.842009e-03
[9551] 2.438511e-03 3.890614e-03 2.320800e-03 3.130022e-03 1.336328e-02
[9556] 5.988376e-03 5.669507e-03 7.208309e-03 6.503248e-03 1.262026e-02
[9561] 2.218269e-03 3.373597e-04 5.694056e-04 1.081303e-02 1.023297e-02
[9566] 3.816400e-03 2.595592e-02 2.476696e-03 9.010793e-03 1.245092e-02
[9571] 1.132183e-02 1.230676e-04 3.586659e-03 5.117296e-03 5.321998e-03
[9576] 9.857871e-03 6.962656e-03 2.298199e-03 1.277160e-02 2.358721e-03
[9581] 1.152802e-02 2.717412e-02 1.379156e-03 7.275407e-03 4.865671e-03
[9586] 3.912963e-04 5.252942e-03 9.484933e-03 7.497268e-03 3.041629e-03
[9591] 2.205159e-03 1.967493e-02 7.444291e-03 1.236535e-02 8.881596e-03
[9596] 1.459450e-03 4.062437e-03 8.173692e-03 1.464456e-02 8.023477e-03
[9601] 1.040646e-02 1.634425e-02 1.439397e-02 1.101019e-02 3.222473e-03
[9606] 1.328417e-03 2.443314e-04 1.020275e-02 4.649800e-03 3.064661e-03
[9611] 5.509205e-03 6.298598e-03 8.708128e-03 1.832598e-03 1.177133e-02
[9616] 6.133768e-03 1.451670e-03 1.916752e-02 5.158346e-03 8.998571e-03
[9621] 7.718261e-03 1.057503e-02 8.626874e-03 2.186229e-02 2.181542e-03
[9626] 3.603593e-03 7.300617e-03 5.112677e-03 5.704457e-03 1.057439e-02
[9631] 2.655753e-03 4.179035e-03 4.434530e-03 1.511362e-02 2.139207e-02
[9636] 2.243621e-02 1.151867e-02 2.323268e-03 1.516385e-03 3.191418e-03
[9641] 3.146940e-02 1.808434e-03 1.430151e-02 8.785998e-03 1.796336e-03
[9646] 1.468104e-02 1.367988e-02 6.605003e-03 1.094973e-02 3.214952e-03
[9651] 1.009544e-02 9.663206e-03 4.232566e-04 1.044611e-03 3.267248e-03
[9656] 4.816311e-03 7.026050e-03 1.176308e-02 3.582679e-03 1.447812e-02
[9661] 5.468275e-03 5.256876e-03 6.973146e-04 2.031343e-02 1.307416e-02
[9666] 7.731806e-04 4.443795e-03 4.481308e-03 1.939465e-02 8.708232e-04
[9671] 4.224543e-03 1.391341e-02 1.958589e-03 7.276533e-03 6.245777e-03
[9676] 8.184682e-03 3.248839e-03 7.195891e-03 3.503934e-03 1.852138e-02
[9681] 1.061781e-02 1.574325e-03 5.019339e-03 1.335595e-02 1.355252e-02
[9686] 8.295893e-03 7.153027e-03 5.441544e-03 4.410930e-03 1.694229e-02
[9691] 4.693069e-03 6.590909e-03 2.028316e-02 7.790482e-03 1.217183e-02
[9696] 1.784228e-02 2.830809e-03 1.173258e-02 1.019886e-02 1.627019e-02
[9701] 3.409380e-03 5.192286e-03 5.582818e-03 1.163472e-02 7.470339e-03
[9706] 7.380444e-03 6.861414e-03 1.356818e-02 8.292100e-04 2.226075e-02
[9711] 5.804008e-03 4.251045e-03 6.197307e-03 4.776887e-03 6.717771e-03
[9716] 4.749855e-03 3.919175e-03 5.294907e-03 1.899160e-02 6.054610e-03
[9721] 6.783952e-03 1.513087e-02 5.801716e-04 7.849905e-03 8.497885e-03
[9726] 2.680000e-03 1.023699e-02 1.176753e-02 1.901606e-02 5.669094e-03
[9731] 1.654147e-03 6.545711e-03 1.141706e-02 1.303370e-02 1.052248e-03
[9736] 5.796636e-03 1.134428e-02 1.144165e-02 7.064123e-03 2.802718e-03
[9741] 1.579973e-02 4.800136e-03 4.047794e-03 3.905346e-03 1.008184e-03
[9746] 1.771978e-03 2.158570e-03 1.565121e-03 1.042717e-03 4.492687e-03
[9751] 1.912393e-03 1.510777e-02 4.147431e-03 3.523448e-03 7.261760e-03
[9756] 8.660640e-03 2.928254e-03 7.796840e-03 1.208016e-02 1.042547e-02
[9761] 2.975309e-04 5.253772e-03 2.497147e-03 1.840153e-03 3.050273e-03
[9766] 1.742313e-03 6.707707e-03 8.741609e-04 7.273894e-04 9.870003e-03
[9771] 3.052128e-03 1.456633e-02 1.228940e-03 1.090583e-02 8.650272e-04
[9776] 1.088110e-02 7.436754e-03 2.553692e-03 1.160970e-02 1.992507e-02
[9781] 8.293383e-03 8.128556e-03 5.511871e-03 1.169109e-02 2.341611e-02
[9786] 2.439338e-02 1.985697e-03 1.686294e-04 5.025083e-03 4.676126e-04
[9791] 3.701429e-03 2.652502e-03 9.081326e-04 2.109601e-02 3.615003e-03
[9796] 1.188888e-02 1.392608e-02 1.930690e-02 5.486570e-03 2.473939e-03
[9801] 5.312653e-03 7.082750e-03 1.302943e-02 2.045143e-04 5.230734e-03
[9806] 2.818965e-02 1.900285e-03 1.757753e-02 7.631166e-03 1.171675e-02
[9811] 1.344359e-02 1.646556e-02 6.977803e-03 6.901469e-03 3.100833e-04
[9816] 1.041844e-02 5.191169e-04 7.707961e-03 1.180384e-02 6.699214e-04
[9821] 7.702564e-03 6.174842e-03 5.028383e-03 7.289655e-03 1.513546e-02
[9826] 1.563393e-02 2.282453e-02 6.885648e-03 1.854525e-02 1.112655e-03
[9831] 2.738433e-03 1.484547e-02 1.859610e-03 7.496199e-03 1.250617e-03
[9836] 5.757158e-03 1.371657e-02 1.075200e-02 1.251127e-03 1.340819e-02
[9841] 2.149349e-03 2.042373e-02 1.300694e-02 1.464101e-02 9.826484e-03
[9846] 4.320343e-04 2.461153e-03 1.712749e-02 5.607354e-03 4.618405e-03
[9851] 7.914414e-03 4.032283e-03 1.268414e-03 1.439909e-02 1.735908e-03
[9856] 2.653683e-02 2.405839e-03 1.371111e-02 1.413273e-02 1.606601e-02
[9861] 9.292876e-03 1.200988e-02 1.077685e-02 2.356685e-02 7.659836e-04
[9866] 1.088137e-02 1.868753e-02 2.188164e-02 1.708929e-02 8.253350e-03
[9871] 2.457955e-04 2.157997e-04 6.461026e-03 1.016472e-02 3.487875e-02
[9876] 3.104715e-03 1.195538e-03 4.799425e-03 8.636037e-03 1.592144e-02
[9881] 1.065687e-02 2.300037e-03 8.178252e-03 1.058082e-02 5.090404e-03
[9886] 8.384524e-03 3.852892e-03 1.572073e-04 9.484937e-03 1.738460e-02
[9891] 6.933686e-03 1.590584e-02 1.140105e-02 3.312895e-03 7.452915e-03
[9896] 1.348474e-02 6.133671e-03 3.610283e-03 1.527912e-02 1.483189e-02
[9901] 9.333148e-03 2.996919e-03 1.014354e-02 3.007416e-03 1.152572e-02
[9906] 1.480537e-02 2.821582e-03 3.391187e-03 5.187638e-03 9.014702e-03
[9911] 6.807090e-03 6.697822e-03 2.393253e-03 1.542971e-02 3.519311e-05
[9916] 4.042427e-03 2.184267e-03 4.129523e-03 1.575967e-02 1.332530e-03
[9921] 1.008013e-02 1.723743e-02 1.117317e-02 5.398630e-03 3.721775e-03
[9926] 3.821677e-03 1.223734e-02 7.123610e-03 2.596568e-03 1.395849e-03
[9931] 1.524500e-02 1.185167e-02 6.469333e-04 2.241790e-02 1.877945e-02
[9936] 5.437215e-04 9.266851e-03 8.985698e-03 2.654650e-03 2.310146e-02
[9941] 1.125526e-02 1.160920e-02 5.845634e-03 7.741253e-03 2.512970e-02
[9946] 6.471816e-03 6.587674e-03 1.562668e-02 2.096587e-02 2.122590e-03
[9951] 2.806544e-03 1.924387e-02 1.158080e-02 1.768886e-02 2.580053e-02
[9956] 2.943419e-03 3.466083e-03 1.021068e-02 4.205045e-03 6.581726e-03
[9961] 1.001645e-02 5.894553e-03 6.122156e-03 5.771906e-03 2.059132e-03
[9966] 3.354054e-03 5.744471e-03 2.846120e-03 1.769083e-02 1.784584e-02
[9971] 8.291330e-03 3.138023e-03 3.955337e-03 1.974376e-03 3.567775e-03
[9976] 3.272548e-03 1.348888e-03 4.216203e-04 2.078729e-02 1.212199e-02
[9981] 1.466101e-02 1.582773e-03 1.511388e-02 1.761366e-02 5.115889e-03
[9986] 1.294019e-02 2.692545e-03 7.323368e-03 4.578742e-03 5.900503e-04
[9991] 3.235725e-03 1.514181e-02 6.255318e-03 5.648119e-03 1.404659e-02
[9996] 9.303810e-03 9.107345e-03 2.008989e-02 9.207495e-03 3.954137e-030.1 f. The ratio difference determines that the it would be safe to assume that the values are independent
Two college students collected data on the price of hardcover textbooks from two disciplinary areas: Mathematics and the Natural Sciences, and the Social Sciences (Hien and Baker (2010)). The data are in the file
BookPrices.Perform some exploratory data analysis on book prices for each of the two disciplinary areas.
Bootstrap the mean of the book price for each area separately and describe the distributions.
Bootstrap the ratio of means. Provide plots of the bootstrap distribution and comment.
Find the 95% bootstrap percentile interval for the ratio of means. Interpret this interval.
What is the bootstrap estimate of the bias? What fraction of the bootstrap standard error does it represent?
BookPrices <- read.csv("http://www1.appstate.edu/~arnholta/Data/BookPrices.csv")
math <- BookPrices %>%
filter(Area == "Math & Science")
social <- BookPrices %>%
filter(Area == "Social Sciences")Your answers:
# Your code here
oMean <- mean(math$Price)
oMean[1] 156.7341oSD <- sd(math$Price)
oSD[1] 39.14483oSMean <- mean(social$Price)
oSMean[1] 98.99oSSD <- sd(math$Price)
oSSD[1] 39.14483oRatio <- oMean / oSSD# Your code here
N <- 10^4
mathBook <- numeric(N)
socialBook <- numeric(N)
for(i in 1: N)
{
mathBook[i] <- mean(sample(math$Price, length(math$Price), replace = TRUE))
socialBook[i] <- mean(sample(social$Price, length(social$Price), replace = TRUE))
}
hist(mathBook)
hist(socialBook)
Both have normal distrubitions with an even spread. Math has an sd of 7.423456 and Social Science has an sd of 17.08938. c.
# Your code here
ratio <- mathBook / socialBook
hist(ratio)
The ratio is even and unimodal with a mean at 1.562375 and has an sd of 0.3431524.
# Your code here
confidence <- quantile(ratio, c(.05, .95))I am 95% certain that the ratio of means of the price of the two textbooks in their respective fields is between 1.212435 and 2.2457324.
# Your code here
mean(ratio) - oRatio [1] -2.369216abs((mean(ratio) - oRatio) / (sd(ratio)*100)) [1] 0.07331349