The annual dividend rates for a random sample of 16 companies in three different industries,utilities,banking,and insurance,were recorded. The ANOVA comparing the mean annual dividend rate among three industries rejected the null hypothesis that the dividend rates were equal. The mean square error (MSE)was 3.36. The following table summarized the results: Based on the comparison between the mean annual dividend rate for companies in the utilities and insurance industries,________.
A)a confidence interval shows that the mean annual dividend rates are not significantly different
B)the ANOVA results show that the mean annual dividend rates are significantly different
C)a confidence interval shows that the mean annual dividend rates are significantly different
D)the ANOVA results show that the mean annual dividend rates are not significantly different

Question

The annual dividend rates for a random sample of 16 companies in three different industries,utilities,banking,and insurance,were recorded. The ANOVA comparing the mean annual dividend rate among three industries rejected the null hypothesis that the dividend rates were equal. The mean square error (MSE)was 3.36. The following table summarized the results:  Based on the comparison between the mean annual dividend rate for companies in the utilities and insurance industries,________.
A)a confidence interval shows that the mean annual dividend rates are not significantly different 
B)the ANOVA results show that the mean annual dividend rates are significantly different 
C)a confidence interval shows that the mean annual dividend rates are significantly different 
D)the ANOVA results show that the mean annual dividend rates are not significantly different

Quizplus · Accepted Answer

Since the ANOVA rejected the null hypothesis, we know that at least one of the mean annual dividend rates among the three industries is significantly different. Since we are comparing the mean annual dividend rates for companies in the utilities and insurance industries, we need to conduct a t-test or calculate a confidence interval to determine if their means are significantly different. Since the question does not mention a t-test, we can assume that a confidence interval is the appropriate statistical tool. If the confidence interval for the difference in means does not include 0, then we can conclude that the means are significantly different. Therefore, the correct answer is C.

The Annual Dividend Rates for a Random Sample of 16