Quiz 2-Chapter 2

library(tidyverse)
library(openintro)
data("df")

## Warning in data("df"): data set 'df' not found

data("i_COHb")

## Warning in data("i_COHb"): data set 'i_COHb' not found

data("seeds")

## Warning in data("seeds"): data set 'seeds' not found

data("plantGrowth")

## Warning in data("plantGrowth"): data set 'plantGrowth' not found

Question 1

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

i_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")

df <-data.frame(i_COHb)
print(df)

##    i_COHb
## 1     6.4
## 2     2.6
## 3     3.5
## 4     2.9
## 5     3.9
## 6     2.2
## 7     5.5
## 8     4.4
## 9     3.5
## 10    3.2
## 11    2.8
## 12    2.4
## 13    3.5
## 14    3.3
## 15    3.7
## 16    2.6
## 17    3.5
## 18    4.5
## 19    4.2
## 20    2.9
## 21    3.1
## 22    3.3
## 23    4.3
## 24    2.6
## 25    4.1
## 26    3.7

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

**Answer: The mean, median, standard deviation, and IQR are as follows:

[1] The mean value of the sample of pregnant women: x̄=3.561538 [1] The median value of the sample of pregnant women: x͂= 3.5 [1] SD= 0.9533423 [1] IQR = 1.15

# Convert from char to numeric; find mean, median, standard deviation and IQR
i_COHb <- as.numeric(i_COHb)
mean(i_COHb)

## [1] 3.561538

median(i_COHb)

## [1] 3.5

sd(i_COHb)

## [1] 0.9533423

IQR(i_COHb)

## [1] 1.15

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

**Answer: See below - added 95% confidence intervals for the median using notch argument;added legend. I was able to add a main label to my box plot, however the code for adding a label on the horizontal and vertical sides of the plot didn’t work.

df <- as.numeric(i_COHb)
boxplot(df, notch=TRUE)

boxplot(df,                                               
     main = "Percent Increase of COHb in Pregnant Smokers")
# legend
legend("topright", legend = "Boxplot", 
    fill = rgb(1, 0, 0, alpha = 0.4),  # Color
    inset = c(0.03, 0.05), # Modify margins
    bg = "white") # Legend background color

3. 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).

**Answer: See below (worth noting - I used ggplot for the Probability lab and had no problem. For some reason, I kept erroring out when using it in various places during the quiz, so I used other code instead.

hist(df,                                                # Change number of histogram breaks
     breaks = 50)

hist(df,                                                # Change main title of histogram
     main = "Percent Increase of COHb in Pregnant Smokers")
lines(density(df), col = "red")                         # Overlay density on histogram

Question 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 (〖cm〗^2 ) 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.

**Answer: See below; the constant, x (13 types of seedlings), is on the X axis; y is the dependent variable, growth. I used several variations of the lines() functionality to overlay a regression line. The plot looks different than I expected, so I tried multiple

samples <- c("1", "2","3", "4","5","6", "7", "8", "9", "10", "11", "12", "13")
lowLight <-c("264","200","225","268","215","241","232","256","229","288","253","288","230")
mLight <-c("314","320","310","340","299","268","345","271","285","309","337","282","273")
plantGrowth <- data.frame(samples, lowLight, mLight)
print(plantGrowth)

##    samples lowLight mLight
## 1        1      264    314
## 2        2      200    320
## 3        3      225    310
## 4        4      268    340
## 5        5      215    299
## 6        6      241    268
## 7        7      232    345
## 8        8      256    271
## 9        9      229    285
## 10      10      288    309
## 11      11      253    337
## 12      12      288    282
## 13      13      230    273

#create scatterplot of data
set.seed(1)
x=samples
y=lowLight
group <- as.factor(ifelse(x < 0.5, "Group 1", "Group 2"))
plot(x, y, pch = as.numeric(group), col = group)

plot(x, y, pch = 19, col = "gray52")
# Underlying model
lines(seq(0, 1, 0.05), 2 + 3 * seq(0, 1, 0.05)^2, col = "2", lwd = 3, lty = 2)
# Linear fit
abline(lm(y ~ x), col = "orange", lwd = 3)

## Warning in abline(lm(y ~ x), col = "orange", lwd = 3): only using the first two
## of 13 regression coefficients

lines(lowess(x, y), col = "blue", lwd = 3)

# Legend
legend("topleft", legend = c("Theoretical", "Linear", "Smooth"),
       lwd = 3, lty = c(2, 1, 1), col = c("red", "orange", "blue"))

# Add new variable (moderate light)
x2=samples
y2=mLight
points(x2, y2, col = "green", pch = 19)
# Linear fit
abline(lm(y2 ~ x2), col = "red", lwd = 3)

## Warning in abline(lm(y2 ~ x2), col = "red", lwd = 3): only using the first two
## of 13 regression coefficients

lines(lowess(x2, y2), col = "yellow", lwd = 3)

Question 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.

**Answer: The histogram shows a median value of 45 with data points between 25 and 60. Box plot C shows the same data.