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 result rejected the null hypothesis that the dividend rates were equal, we know that at least one of the mean annual dividend rates is significantly different. To compare the mean annual dividend rates for companies in the utilities and insurance industries, we would need to conduct a post-hoc test or calculate a confidence interval. Since there is no information given about a post-hoc test, we can only assume that a confidence interval was calculated and found to show that the mean annual dividend rates for these two industries are significantly different. Therefore, the best choice is C.

The Annual Dividend Rates for a Random Sample of 16