statistics with R programming

Assignment 5, STA 610, Fall 2020

As always, when asked to use samples to learn about populations, you need to do a confidence interval or hypothesis test. When there is no mention of a CI, you are being asked to do a hypothesis test, which means addressing (and labeling) the 8 steps as discussed in class. As always, you should include R code and output as showing work if your answers are based on R output. You should calculate all test statistics by hand for the purposes of this assignment, but you are welcome to confirm the value with R. You can use R for p-values (or calculator where relevant), but you should include R code and output to support your answer.

1. Consider #5 on pages 241-242 in the Aho textbook. Do not follow their parts (a) through (g), and do not assume the population variances are equal. The data are on BB so you don’t have to extract from R, but they are also found in R if you can load the asbio package.

(a) Determine if there is evidence in the sample that the O2 level below the town is lower than above the town, on average, in the populations. Regardless of your assessment of the conditions, assume both populations are normal in step 1 (after checking sample sizes and sample shapes).

(b) Calculate and interpret a 95% confidence interval for the difference in population means (assuming both populations are normal).

(c) Explain how this confidence interval could be used to decide whether or not to reject the null hypothesis in 1a.

(d) Redo only steps 2, 3, 4, and 5 from 1a without assuming the populations are normal, but instead assuming the populations have the same shape and variability.

2. Consider #7 on page 242 in the Aho textbook. Do not follow their parts (a) through (e). Note that the same variable was observed on each subject twice (which is why they are listing X – Y), and this must be taken into account.

(a) Determine if there is evidence in the sample that program X is superior to program Y, on average, in the population. Regardless of your assessment of the condition, assume the population is normal in step 1 (after checking sample size and sample shape).

(b) Redo only steps 2, 3, 4 and 5 from 2a, but now assuming the population is symmetric.

(c) Redo only steps 2, 3, 4 and 5 from 2a, but now assuming the population is not symmetric.