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 alpha = 0.05, can you reject the claim that the mean numbers of female students who played on a sports team are equal for all grades? Perform a one-way ANOVA test by completing parts a through d. Assume that each sample is drawn from a normal population, that the samples are independent of each other, and that the populations have the same variances. c. H_0: mu_1 = mu_2 = mu_3 = mu_4 H_a: At least one mean is different from the others. H_0: mu_1 = mu_2 = mu_3 = mu_4 = mu_5 = mu_6 H_a: At least one mean is different from the others (claim) (b) Identity the degrees of freedom for the numerator and forth denominator, determine he critical value, and determine the rejection region. The degrees of freedom for the numerator, d f_N, is and the degrees of freedom for the denominator, d. f_D is The critical value is F_O = (Round to two decimal places as needed.) The rejection region is F > 3.10. (Round to two decimal places as needed.) (c) Calculate the test statistic. (Round to three decimal places as needed.)

Explanation / Answer

(a) is Option C

(b) df numerator = c-1 = 4-1 = 3, df denominator = N-c = 24-4 = 20

Fcritical at 0.05,3,20 = 3.098 = 3.1(approximately)

The rejection region F>3.1

(c) The tables below give the value of the F stat

F stat = 0.304

Mean(x bar) 84 80.67 77.5 72.17 SD 25.799224 23.6784 20.51097 18.81931 Variance 665.60 560.67 420.70 354.17 n 6 6 6 6 columns 4

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