Question

1. Finally, you have been asked to compare the mean ages of the supporters of the candidate in various sectors of the country. Random samples of supporters of the candidate are selected from five geographic areas. The data that has been collected is shown in appendix four below. At the 5% level of significance, are there any differences in the mean ages of the supporters of the candidate based on their residencies? If you do find any differences in the mean ages, do the work necessary to find where those differences lie. As a further part of your work, perform the necessary test to ascertain whether the necessary quality of homogeneity of variances exists.

Appendix Four:

                                                                      Region

            Supporter      North       East         South              West               Midwest

       1              23             36              45                 22                      40

       2              66             50              48                  51                      75

       3              43             40              29                  52                      65

       4              70             28              30                  31                      30

       5              60             26              38                35                      67

       6              49             34              87                65                      78

       7              54             59            20                 19                      67

       8              64           51              26                29                      76

       9              54             50              39                43                      44

      10             60             42              38                54                      61

      11             70             58              50                48                      70

      12             49             48              29                18                      90

      13             38             37              21                34                      78

      14             40             31              29                30                      69

      15             49             52              40                50                      28

Answer 1

One-way ANOVA: Age versus Region

Source	DF	SS	MS	F	P
Region	4	6612	1653	7.50	0.000
Error	70	15418	220
Total	74	22030

S = 14.84 R-Sq = 30.01% R-Sq(adj) = 26.01%

Comment: The p-value for the F-test at the above ANOVA table is 0.000 and less than 0.05 level of significance. Hence, we can conclude that at least one mean age of a region is significantly different from the remaining region at 0.05 level of significance. So, this accepts the differences in the mean ages of the supporters of the candidate based on their residencies

From the posthoc test, the differences in the mean ages are happening between the regions: East & Midwest, Midwest & South, and Midwest & West.

The p-value for Bartlett's Test statistic is 0.314 and less than 0.05 level of significance. Hence, we can accept the homogeneity of variances of ages between the regions at the 0.05 level of significance.