Consider the following information.
SSTR = 6750
H₀: μ₁ =μ₂ =μ₃ =μ₄= μ₅
SSE = 8000
H_a: At least one mean is different

The test statistic to test the null hypothesis equals

Question

Quizplus · Accepted Answer

The test statistic for an ANOVA test is calculated as F = (SSTR / k-1) / (SSE / n-k), where k is the number of treatment groups and n is the total sample size. Here, SSTR = 6750, SSE = 8000, k = 5 (based on the notation H₀, H₁, H₂, H₃, and H₄), and n is not provided. Since we cannot determine n from the information given, we cannot calculate the exact value of F or determine the degrees of freedom for the numerator and denominator for the F-distribution. However, we can determine whether the null hypothesis (that all means are equal) should be rejected based on the value of F at a certain significance level. Using a significance level of 0.05, the critical value of F with 4 and n-5 degrees of freedom (based on k-1 = 4 and n-k = dfE) is approximately 2.87. Since F > 2.87 would lead to rejection of the null hypothesis, and 4.22 > 2.87, we can conclude that the null hypothesis should be rejected and that at least one mean is significantly different from the others. Therefore, the best choice is C.

Consider the Following Information. ​

Consider the Following Information.