1. The carbon monoxide in cigarettes is thought to be hazardous to the fetus of a pregnant woman who smokes. In a study of this hypothesis, blood was drawn from pregnant women before and after smoking a cigarette. Measurements were made of the percent increase of blood hemoglobin bound to carbon monoxide (COHb). The results for 26 women are: # 6.4 2.6 3.5 2.9 3.9 2.2 5.5 4.4 3.5 3.2 2.8 2.4 3.5 # 3.3 3.7 2.6 3.5 4.5 4.2 2.9 3.1 3.3 4.3 2.6 4.1 3.7

#create vector COHb

COHb <-c(6.4,   2.6,    3.5,    2.9,    3.9,    2.2,    5.5,    4.4,    3.5,    3.2,    2.8,    2.4,    3.5,3.3,    3.7,    2.6,    3.5,    4.5,    4.2,    2.9,    3.1,    3.3,    4.3,    2.6,    4.1,    3.7)

a) Find the mean, median, sample standard deviation, and IQR. Be sure to include proper STATISTICAL notation for each with their respective values

summary(COHb)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   2.200   2.900   3.500   3.562   4.050   6.400

Min 2.2

1st quartile = 2.9

median x-tilde = 3.5

mean x-bar = 3.562

3rd Quartile = 4.05

Max = 6.4

range = 4.2

calculate IQR = Q3-Q1

IQRCOHb <-sum(4.05-2.9)
print(IQRCOHb)
## [1] 1.15

IQR is 1.15.

calculate sdCOHb

sdCOHb <-sd(COHb)
print(sdCOHb)
## [1] 0.9533423

SD = 0.9533423

range(COHb)
## [1] 2.2 6.4

###create frequency distribution

breaks = seq(2,6.5, by = 0.84)
COHb.cut=cut(COHb, breaks, right = FALSE)
COHb.freq=table(COHb.cut)
cbind(COHb.freq)
##             COHb.freq
## [2,2.84)            6
## [2.84,3.68)        10
## [3.68,4.52)         8
## [4.52,5.36)         0
## [5.36,6.2)          1

b) Create a boxplot of these observations. create

boxplot(COHb, data= COHb, main="boxplot of % increase COHb in pregnant women using tobacco", xlab = "% change COHb",horizontal = TRUE)
abline(v=summary(COHb), col= "blue", lwd = 0.5)

there is one outlier

c. Create a histogram of these observations. If you are not using R, be sure your axis shows a proper scale (R will display the scale by default).

breaks = seq(2,6.5, by = 0.84)

hist(COHb, breaks = seq(2,7,by =0.83), col = "maroon", main = "Histogram of % increase COHb in pregant smoking women ")
abline(v=summary(COHb), col= "blue", lwd = 0.5)  # this displays 5 # summary on histogram

###interpretation - the dataset COHb is unimodal and skewed the right.the median y~= 3.5 is a better measure of central tendency compared to mean x bar = 3.522 as the median is more resistant to the right pull of the outlier compared to the mean.

2. A plant physiologist investigated the effect of light on the growth of soybean plants. 13 different types of soybean seedlings were randomly allocated to two treatments: low light and moderate light. After 16 days of growth, plants were harvested, and the total leaf area cm2 of each plant was measured. In the space below, create a scatterplot of the data. Try to include axes labels on each of the axes. If you can, overlay a regression line on your scatterplot.

generate scatterplot with low light on x axis and moderate light on y axis. Add a linear regression line

lowlight <- c(264,200,225,268,215,241,232,256,229,288,253,288,230)
mediumlight <- c(314,320,310,340,299,268,354,271,285,309,337,282,273)

#generate histograms to assess the distribution

hist(lowlight)

hist(mediumlight)

plot(x=lowlight, y=mediumlight, main="scatterplot soybean leaf growth(cm2) lowlight vs moderate at 16 days ", xlab="lowlight", ylab="mediumlight")   
abline(lm(mediumlight~lowlight), col="red")  # regression line (y~x)

calculate correlation coefficient using cor fx(independent, dependent)

cor(lowlight,mediumlight)
## [1] -0.02651767

r coefficient is negative and suggests an indirect relationship.

3. The following histogram shows the same data that are shown in one of the four boxplots. Which boxplot (a, b, c, or d) goes with the histogram? Explain your answer.

ANS: boxplot a) appears to match the histogram distribution most closely. the range is the same at min = 25 and max = 65, the fulcrum point of the histogram is approximately around bin 35-40. The median for boxplot a) is 35. therefore boxplot a) most closely matches the histogram.