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: The interval is [3.38, 8.18]. 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:  The interval is [3.38, 8.18]. 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 analysis rejected the null hypothesis that the dividend rates were equal, we know that at least one pair of industries have significantly different mean annual dividend rates. Therefore, we need to perform a pairwise comparison between the utilities and insurance industries. The confidence interval shows that the mean annual dividend rates for these industries are significantly different because the interval does not include zero, which indicates that the difference is statistically significant.

The Annual Dividend Rates for a Random Sample of 16