Question

The following table is a summary of randomly chosen student evaluations of faculty at a university over a three-year period. The researcher is interested in whether the distribution of evaluations differs by faculty rank. Rank Evaluation Professor Assistant Professor Associate Professor Total Above Average 48 39 36 123 Below Average32 31 54 Total 80 70 90 240

Q1: In analysis of variance, which of the following is true if the F statistic is Zero?

1) All of sample means are equal

2) All of the sample variances are equal

3) The F statistic can't be zero, duh

4) at least one of the poputlation means is different

Answer 1

H_0: The distributions are same for all populations H_1: The distributions are not same for all populations We calculate expected frequencies by: E = (Row Total) (Column Total)/Grand Total To calculate chi-square test statistic we calculate this formula on each cell: (Observed Count - Expected Count)^2/Expected Count Test statistic: chi^2 = 7.569 Significance level = 0.05 (default value) Degrees of freedom, df = (r - l)(c - 1) = (2 - 1) * (3 - 1) = 2 Critical value: chi^2_0.05 = 5.991 X^2_0 05 has area of 0.05 to its right. To find chi^2_0.05, open any Chi-square table, go across from row df = nu = 2 and down from column 0.05 and get 5.991 To get p-value, we can use excel function CHISQ.DIST.RT (7.569 016, 2) = 0.022 720 034 almostequalto 0.0227 Since test statistic is greater than critical value, we reject null hypothesis. At 5% level, there is sufficient evidence that the distributions are significantly different