1. Baseball Controversy : In recent years a controversy has arisen in major league baseball. Some players have been accused of "doctoring" their bats to increase the distance the ball travels. However, a physics professor claims that the effect of doctoring, no matter how it is done, is negligible. A major league manager decides to test the professor’s claim considering two different types of doctoring. He doctors two bats by inserting cork into one and rubber into another. He then selects five players on his team and has them each hit a ball with an un-doctored bat and with each of the doctored bats. The distances are measured and listed below.
   
   
   
   We can assume that the data are normally distributed and that the variances
   for each treatment are equal. BE SURE TO USE THE CORRECT EXPERIMENTAL
   DESIGN
   
   a.) Do these data provide sufficient evidence at a 5% level of significance
   to refute the professor’s claim?
   
   b.) Does our result indicate the need for any multiple comparison testing?
   Why? If yes, do it. (Use \(\alpha \) = 0.05). You must show all seven steps.
   c.) Does the experimental design suggest any additional hypothesis tests
   that could be done? If yes, do them (use alpha = 0.05).
   
2. 
   A recent college graduate is in the process of deciding which one of three graduate schools he should apply to. He decides to judge the quality of the schools on the basis of the Graduate Management Admission Test (GMAT) scores of those who are accepted into the school. A random sample of six students in each school produced the following GMAT scores. Assume that the data are normally distributed and that the variances are equal -- all required conditions are met.
   

a.) Can he infer at the 10% significance level that the GMAT scores differ
among the three schools?

b.) Does our result indicate the need for any multiple comparison testing?
Why? If yes, do it. Use \(\alpha \) = 0.10. You must show all seven steps.

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