A survey looked at the value of recreational sports on college campuses. One of

Question

A survey looked at the value of recreational sports on college campuses. One of the questions asked each student to rate the importance of recreational sports to college satisfaction and success. Responses were on a 10-point scale with 1 indicating total lack of importance and 10 indicating very high importance. The following table summarizes these results: Class n Mean score Freshman Sophomore Junior Senior 722 535 591 438 7.6 7.6 7.5 7.3 (a) To compare the mean scores across classes, what are the degrees of freedom for the ANOVA F statistic? numerator df denominator df (b) The MSG = 11.406. If sp = 2.12, what is the F statistic? (Round your answer to two decimal places.) F = (c) Give an approximate (from Table E) or exact (from software) P-value. (Enter your answer to four decimal places.)

Explanation / Answer

Answer

Part a)

numerator df is k-1 ,where k is number of categories 4-1 = 3

denominator df is n-k , where n = 722+535+591+438 - 4 =2282

Part b)

given MSG = 11.406 and Sp = 2.12 so MSE = Sp^2

= MSE = 2.12^2 = 4.4944

so F stat = MSG/MSE = 11.406/4.4944 = 2.5378

Part c)

so the p value is 0.054985 at an alpha of 0.05 df1 = 3 and df2 = 2281 and F stat = 2.4739

The p-value is .054985. The result is not significant at p < .05.

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