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Statistics Statistics Level: University

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. Distance Ball Travels (in feet)
 Player Un-doctored Bat Bat with Cork Bat with Rubber 1. 275 265 280 2. 315 335 320 3. 425 435 440 4. 380 375 370 5. 450 460 450
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 α = 0.05). You must show all seven steps.