One-way analysis of variance is being used to test the equality of three population means using a sample of size 12 from each of the three populations.The between groups sum of squares (SSB) is 4,250 and the within groups sum of squares (SSW) is 33,660.The test statistic (F_stat) is A)7.920 B)2.083 C)0.126 D)4.617

Question

Quizplus · Accepted Answer

The test statistic for ANOVA is calculated as the ratio of the mean square between groups (MSB) to the mean square within groups (MSW). MSB is calculated as SSB / (k - 1) and MSW is calculated as SSW / (N - k), where k is the number of groups and N is the total sample size. Here, k = 3 (three populations) and N = 36 (12 samples from each of the three populations).First, calculate MSB and MSW:- MSB = SSB / (k - 1) = 4,250 / (3 - 1) = 4,250 / 2 = 2,125.- MSW = SSW / (N - k) = 33,660 / (36 - 3) = 33,660 / 33 = 1,020.Then, calculate the F statistic:- F = MSB / MSW = 2,125 / 1,020 ≈ 2.083.Therefore, the correct answer is B, 2.083.

One-Way Analysis of Variance Is Being Used to Test the Equality