Suppose the accompanying summary statistics for a measure of social marginality for samples of youths, young adults, adults, and seniors appeared in a research paper. The social marginality score measured actual and perceived social rejection, with higher scores indicating greater social rejection. Age Group Youths Young Adults Adults Seniors
Sample Size 102 258 319 31
x :2.00 3.10 3.06 2.81
s :1.59 1.66 1.69 1.87
For purposes of this exercise, assume that it is reasonable to regard the four samples as representative of the U.S. population in the corresponding age groups and that the distributions of social marginality scores for these four groups are approximately normal with the same standard deviation. Is there evidence that the mean social marginality scores are not the same for all four age groups? Test the relevant hypotheses using α = 0.01.
Calculate the test statistic. (Round your answer to two decimal places.) F = ?
What can be said about the P-value for this test?
P-value > 0.100
0.050 < P-value < 0.100
0.010 < P-value < 0.050
0.001 < P-value < 0.010
P-value < 0.001
What can you conclude?
Reject H0. There is not convincing evidence that the mean social marginality scores are not the same for all four age groups.
Reject H0. There is convincing evidence that the mean social marginality scores are not the same for all four age groups.
Fail to reject H0. There is convincing evidence that the mean social marginality scores are not the same for all four age groups.
Fail to reject H0. There is not convincing evidence that the mean social marginality scores are not the same for all four age groups.
You may need to use the appropriate table in Appendix A to answer this question.