It is common for baseball pitchers to use stretching to prepare for a game. But does this make a difference? The authors of the paper ?The Acute Effects of Upper Extremity Stretching on Throwing Velocity in Baseball Throwers? (Journal of Sports Medicine [2013]: 1?7) carried out an experiment to compare two different types of stretching and a control treatment consisting of no stretching. Participants were adult males with varying levels of baseball throwing experience and who were not professional or collegiate baseball players. Participants in the two stretching treatments went through a warm-up that included 8 minutes of stretching. Each participant then threw 10 pitches, and the average speed (km/hour) was calculated.

a. Explain why it is important that the participants be assigned at random to the three different treatment groups (Stretching Method 1, Stretching Method 2, and No Stretching).

b. The following computer output and summary values are based on simulated data that are consistent with information and conclusions given in the paper. Use the given output to determine if there is evidence to support the claim that the means for average speed are not the same for all three treatments. Use a significance level of 0.05 for your test.

c. Previous research on the effect of stretching on performance in other sports, such as running, has concluded that stretching can improve performance. Why do you think that the authors of this paper were surprised by the results of this study?

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Analysis of Variance Source DF Adj ss Adj MS F-Value P-Value Factor 2 1097 548.7 2.44 0.094 Error 78 17570 225.3 Total 80 18667 Means Factor Mean StDev 95$ CI Stretching 27 86.26 15.95 (80.51, 92.01) Method 1 Stretching 27 90.30 17.06 (84.55, 96.05) Method 2 No Stretching 27 95.26 11.42 (89.51, 101.01)