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 = 0.10, 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 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. 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) H_0: mu_1 = mu_2 = mu_3 = mu_4 (claim) H_a: At least one mean is different from the others. (b) Identify the degrees of freedom for the numerator and for the denominator, determine the 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. Enter your answer in the edit fields and then click Check Answer.

Explanation / Answer

In ANOVA, the F stat is found by dividing the between group variance by the within group variance.

The degrees of freedom for the numerator is the degrees of freedom for the between group = c-1, where c is the no of columns.

The degrees of freedom for the denominator, is the total no of values (N) minus the no of columns(k) = N-c

The no of columns here = 4

Each column has 6 values, therefore N = 6*4 = 24

Therefore d.fN = 4-1 = 3 and d.fD = 24-4 = 20

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