Homework 9
Directions
Please turn in this homework on Sakai. You will need to turn in an html file and a qmd file, Please submit your homework in pdf format if you are not rendering a Quarto document. If you are using a Quarto doc to render your full homework, then you can keep it as an html!
You can download the .qmd file for this assignment from Github if you want to work in a Quarto doc. You do not need to work in a Quarto doc for this homework!!
It is a good idea to try rendering your document from time to time as you go along! Note that rendering automatically saves your Qmd file and rendering frequently helps you catch your errors more quickly.
Book exercises
8.28 True or false, Part II
8.34 Coffee and Depression
0.0.1 (a)
0.0.2 (b)-(f)
Instead of doing part (b) - (f), please run a hypothesis test using the Chi-squared test.
0.0.3 (g)
1 R exercise
1.1 Load all the packages you need below here.
2 Nonparametric-Tests
2.1 NPT 1: (Wilcoxon) Signed-rank test
Vegetarian diet and cholesterol levels
When covering paired t-tests on Day 10 Part 2, the class notes used the example of testing whether a vegetarian diet changed cholesterol levels. The data are in the file chol213.csv at https://niederhausen.github.io/BSTA_511_F23/data/chol213.csv. In this exercise we will use non-parametric tests to test for a change and compare the results to the paired t-test.
2.1.1 Hypotheses
What are the hypotheses for the signed-rank test (2-sided) in the context of the problem?
2.1.2 Test in R
Run the (Wilcoxon) Signed-rank test in R. What is the p-value and how does it compare to the p-value of the sign test and the paired t-test (check the class notes for this)?
8.38 (a) & (extra) Salt intake and CVD
Do not do parts (b)-(c) in the book
(a)
- You can use the expected cell counts from
expected()in R (you do not need to compute them using the formula). - Comment on whether the sample size condition is met or not for these data.
(extra)
Run a Fisher’s Exact test. Include the hypotheses and a conclusion in the context of the problem.
3 Extra R exercises (optional)
3.1 R2: Palmer Penguins SLR
Below I frequently use the terminology variable1 vs. variable2. When we write this, the first variable is \(y\) (vertical axis) and the second is \(x\) (horizontal axis). Thus it’s always \(y\) vs. \(x\) (NOT \(x\) vs. \(y\)).
3.1.1 Scatterplots
- For each of the following pairs of variables, make a scatterplot showing the best fit line and describe the relationship between the variables.
- In particular address
- whether the association is linear,
- how strong it is (based purely on the plot), and
- what direction (positive, negative, or neither).
body mass vs. flipper length
bill depth vs. flipper length
bill depth vs. bill length
3.1.2 Correlations
- For each of the following pairs of variables, find the correlation coefficient \(r\).
body mass vs. flipper length
bill depth vs. flipper length
bill depth vs. bill length
3.1.3 Compare associations
Which pair of variables has the strongest association? Which has the weakest? Explain how you determined this.
3.1.4 Body mass vs. flipper length SLR
Run the simple linear regression model for body mass vs. flipper length, and display the regression table output.
3.1.5 Regression equation
Write out the regression equation for this model, using the variable names instead of the generic \(x\) and \(y\), and inserting the regression coefficient values.
3.1.6 Interpret intercept
Write a sentence interpreting the intercept for this example. Is it meaningful in this example?
3.1.7 Interpret slope
Write a sentence interpreting the slope for this example.