Question: Three racquetball players, one from each skill level, have been randomly selected from the membership list of a health club. Using the same ball, each

Three racquetball players, one from each skill level, have been randomly selected from the membership list of a health club. Using the same ball, each person hits five serves, one with each of five racquets, and using the racquets in a random order. Each serve is clocked with a radar gun, and the results are shown here. With player skill level as a blocking variable, use the 0.025 level of significance in determining whether the treatment effects of the five racquets could all be zero. Using the 0.01 level, evaluate the effectiveness of the blocking variable. (Use data file XR12052.)

Player Skill Level Beginner Intermediate Advanced A 73 mph 63 64 mph 72 54 81 90 83 mph 89 72 86 97 Racquet c 51 Model D 56 E 69

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For this problem the five racquet models are the treatments and the three skill levels are the blocks The Minitab printout is shown below Twoway ANOVA mph versus Skill Racquet Analysis of Variance for mph Source DF SS MS F P Skill 2 13321 6661 1344 0003 Racquet 4 10567 2642 533 0022 Error 8 3965 496 Total 14 27853 Testing for treatment effects To determine if the racquet treatment effects could all be zero we test H 0 t j 0 for treatments j 1 2 3 4 5 and H 1 t j 0 for at least one of the treatments The calculated test statistic is Using the F table the critical value is F0025 4 8 505 The decision rule is Reject H 0 if the calculated F 505 otherwise do not reject Since the calculated test statistic falls in the rejection region reject H 0 At the 0025 level we conclude that the treatment effects of the five racquets are not all zero Therefore at the 0025 level the racquet models are not equally effective As shown in the Minitab printout the pvalue for the test of treatment effects is 0022 Testing for block effects H 0 b i 0 for i 1 2 3 the levels of the blocking variable are equal in their effect H 1 b i 0 for at least one value of i at least one level has an effect different from the others For the block ... View full answer

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