Data set: NLBB Salaries
a. Conduct a permutation test to determine if there is a difference in mean salaries between pitchers and first basemen. Report the p-value and your conclusions based on an individual a-level of 0.05.
b. Conduct a permutation test to determine if there is a difference in mean salaries between pitchers and catchers. Report the p- value and your conclusions based on an individual a-level of 0.05.
c. Conduct a permutation test to determine if there is a difference in mean salaries between first basemen and catchers. Report the p- value and your conclusions based on an individual a-level of 0.05.
d. If each of the previous three tests uses an a-level of 0.05, what is the true probability that at least one of the tests will inappropriately reject the null hypothesis?
e. What is the individual critical value if you use the Bonferroni method with an overall (family-wise) a-level of 0.05? Do any of your previous conclusions in the preceding parts of this exercise change if you test for an overall (familywise) comparison? Explain.