A random sample of 16 companies was selected and asked for their annual dividend rate in three different industries: utilities, banking, and insurance. The ANOVA comparing the mean annual dividend rate among three industries rejected the null hypothesis. 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

A random sample of 16 companies was selected and asked for their annual dividend rate in three different industries: utilities, banking, and insurance. The ANOVA comparing the mean annual dividend rate among three industries rejected the null hypothesis. 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 null hypothesis was rejected in the ANOVA, we can conclude that there is significant difference in mean annual dividend rate among the three industries. To compare the difference between utilities and insurance industries, we need to construct a confidence interval. Since the MSE is known, we can use Tukey's HSD post-hoc test to construct the confidence interval. If the confidence interval does not include zero, it indicates that the mean annual dividend rates are significantly different. Therefore, the correct choice is C.

A Random Sample of 16 Companies Was Selected and Asked