Chapter 10.3, Problem 46PB

Compare permutation test to t test Refer to the previous exercise.

1. a. Run a t test and report the P-value for the two-sided alternative hypothesis.
2. b. Using a significance level of 0.10, are the decisions based on the t test and based on the permutation test comparable? Which one would you trust more?
3. c. Remove the largest observations (which could be outliers) in each of the two groups, as was done in Exercise 10.32. Does the conclusion of the permutation test change?

10.45 Time spent on social networks revisited Exercise 10.31 considered the following data on the number of hours students spent on social network sites per week:

Enter the observations (separated by spaces) into the Permutation Test web app. Let males be Group 1 and females be Group 2. We are interested in testing whether the population mean number of hours spent on social networks differs between males and females, using as test statistic the difference in sample means.

1. a. What are the observed group means and their difference? (The subtitle of the dot plot shows this information.)
2. b. Press the Generate Random Permutation(s) button once to generate one permutation of the original data. What are the two group means and their difference under this permutation? (The subtitle of the dot plot shows this information.)
3. c. Did this one permutation lead to a difference that is less extreme, as extreme, or more extreme than the observed difference?
4. d. Select to generate 10,000 random permutations. How many of them resulted in a test statistic as or more extreme than the observed difference? (Remember, the alternative hypothesis is H_a: μ₁ ≠ μ₂.)
5. e. Find and interpret the permutation P-value.