It is common for baseball pitchers to use stretching to prepare for a game. But does this make a difference? The authors of a paper on the effects of stretching in baseball carried out an experiment to compare twodifferent 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 baseballplayers. Participants in the two stretching treatments went through a warm-up that included 8 minutes of stretching. Each participant (all three groups) then threw 10 pitches, and the average speed (km/hour) wascalculated.(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).Random assignment ensures that our experiment systematically favors one experimental condition over all others and attempts to create experimental groups that are as much alike as possible.O Random assignment ensures that our experiment does not systematically favor one experimental condition over any other and attempts to create experimental groups that are as much alike aspossible.Random assignment ensures that our experiment systematically favors one experimental condition over all others and attempts to create experimental groups that are as different as possible.Random assignment ensures that our experiment does not systematically favor one experimental condition over any other and attempts to create experimental groups that are as different as possible.(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 evidenceto support the claim that the mean average speed is not the same for all three treatments. Use a significance level of 0.05 for your test.Analysis of VarianceSource DF Adj ssFactorErrorTotal2727410311624817278MeansFactorStretchingMethod 1StretchingMethod 2No StretchingWhat is the test statistic?F =NAdj MS F-Value515.3225.72.28Mean25 86.21What is the P-value for this test?25 90.3725 95.28St Dev15.9617.0511.47P-Value0.109295% CI(79.62, 92.80)(83.33, 97.41)(90.55, 100.01)State the conclusion in the context of the problem.Fail to reject Ho. The data do not provide convincing evidence that the mean average speed is not the same for all three treatments.O Reject Ho. The data do not provide convincing evidence that the mean average speed is not the same for all three treatments.Fail to reject Ho. The data provide convincing evidence that the mean average speed is not the same for all three treatments.Reject HoThe data provide convincing evidence that the mean average speed is not the same for all three treatments.(c) Previous research on the effect of stretching on performance in other sports, such as running, has concluded that stretching can improve performance. Do you think that the authors of this paper were surprisedby the results of this study?Yes, the authors were probably surprised. This study concludes that there is sufficient evidence that stretching improves performance. These results contradict the results of other studies, which concludedthat stretching can improve performance.Yes, the authors were probably surprised. This study concludes that there is not sufficient evidence that stretching improves performance. These results contradict the results of other studies, whichconcluded that stretching can improve performance.O No, the authors were probably not surprised. This study concludes that there is sufficient evidence that stretching improves performance. These results support the results of other studies, whichconcluded that stretching can improve performance.O No, the authors were probably not surprised. This study concludes that there is not sufficient evidence that stretching improves performance. These results support the results of other studies, whichconcluded that stretching can improve performance.

(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). O Random assignment ensures that our experiment systematically favors one experimental condition over all others and attempts to create experimental groups that are as much alike as possible. O Random assignment ensures that our experiment does not systematically favor one experimental condition over any other and attempts to create experimental groups that are as much alike as possible. O Random assignment ensures that our experiment systematically favors one experimental condition over all others and attempts to create experimental groups that are as different as possible. O Random assignment ensures that our experiment does not systematically favor one experimental condition over any other and attempts to create experimental groups that are as different as possible. (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 mean average speed is not the same for all three treatments. Use a significance level of 0.05 for your test. Analysis of Variance 2 Source DE Adj SS Factor 1031 Error 16248 Total 17278 Means Factor 72 74 N What is the test statistic? F = Adj MS 515.3 225.7 Stretching Method 1 Stretching Method 2 25 90.37 No Stretching 25 95.28 Mean StDev 25 86.21 15.96 (79.62, 92.80) What is the P-value for this test? F-Value 2.28 P-Value 0.1092 17.05 95% CI (83.33, 97.41) (90.55, 100.01) State the conclusion in the context of the problem. O Fail to reject Ho. The data do not provide convincing evidence that the mean average speed is not the same for all three treatments. O Reject Ho. The data do not provide convincing evidence that the mean average speed is not the same for all three treatments. O Fail to reject Ho. The data provide convincing evidence that the mean average speed is not the same for all three treatments. O Reject Ho. The data provide convincing evidence that the mean average speed is not the same for all three treatments. (c) Previous research on the effect of stretching on performance in other sports, such as running, has concluded that stretching can improve performance. Do you think that the authors of this paper were surprised by the results of this study? O Yes, the authors were probably surprised. This study concludes that there is sufficient evidence that stretching improves performance. These results contradict the results of other studies, which concluded that stretching can improve performance. O Yes, the authors were probably surprised. This study concludes that there is not sufficient evidence that stretching improves performance. These results contradict the results of other studies, which concluded that stretching can improve performance. O No, the authors were probably not surprised. This study concludes that there is sufficient evidence that stretching improves performance. These results support the results of other studies, which concluded that stretching can improve performance. O No, the authors were probably not surprised. This study concludes that there is not sufficient evidence that stretching improves performance. These results support the results of other studies, which concluded that stretching can improve performance.