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 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 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

The ANOVA test rejected the null hypothesis that the mean annual dividend rate is the same across all three industries, indicating that there is a significant difference in at least one of the means. To determine if the mean annual dividend rate for companies in utilities and insurance industries are significantly different, we need to conduct a post-hoc analysis or a confidence interval. Since we have no information about the direction of the difference, we need to use a two-sided confidence interval. If the confidence interval does not include zero, then we can conclude that the mean annual dividend rates are significantly different.

A Random Sample of 16 Companies Was Selected and Asked