The table to the right shows the number of female students who played on a sport

Question

The table to the right shows the number of female students who played on a sports team in grades 9 through 12 for a random sample of 6 high schools in a state. At ?= 0.01, can you reject the claim that the mean rade Grade Grade numbers of temale students who played on a sports team are equal tor all grades? Pertorm a one way ANOVA test by completing parts a through d. Assume that each sample is drawn trom a normal population,hat910 11 12 63 58 62 65 64 51 56 49 77 72 80 82 91 87 8177 53 5 46 42 116 109 101 90 the samples are independent of each other, and that the populations have the same vaiances D. Ho: At least one mean is different from the others. (claim) Ha At least one mean is different from the others. (claim) (b) Identify the degrees of freedom for the numerator and for the denominator, determine the critical value, and determine the rejection region The degrees ot treedom for the numerator, d.fy, Is 3, and the degrees ot freedom for the denominator, d.tp, 20 The cnitical value is Fo4.94 (Round to two decimal places as needed.) The rejection region isF4.94 Round to two decimal places as needed.) (c) Calculate the test statistic. (Round to three decimal places as needed.) Enter your answer in the answer box and then click Check Answer

Explanation / Answer

The statistical software output for this problem is:

Analysis of Variance results:
Data stored in separate columns.

Column statistics

ANOVA table

Hence,

F = 0.224

Column n Mean Std. Dev. Std. Error Grade 9 6 77.333333 23.053561 9.4115768 Grade 10 6 72.5 22.024986 8.9916628 Grade 11 6 71 20.05991 8.1894241 Grade 12 6 67.5 19.002631 7.7577918

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