Decision is correct, fail to reject and therefore conclude there is no evidence to suggest the true proportion of women with college degrees is greater than the true proportion of men with college degrees.
I have a problem I am doing for hw for my Data Analysis II course, which involves the use of Minitab and need help. I solved it, but need to know if I had done it correctly.
Problem: A random sample of 78 women ages 21-29 in Denver showed that 23 have a college degree. Another random sample of 73 men in Denver in the same age group showed that 20 have a college degree. Based on information from Educational Attainment in the United States, Bureau of the Census, does this indicate that the proportion of Denver women ages 21-29 with college degrees is more than Denver men in this same age group?
My Minitab output:
Test and CI for Two Proportions
Sample X N Sample p
1 23 78 0.294872
2 20 73 0.273973
Difference = p (1) - p (2)
Estimate for difference: 0.0208992
95% lower bound for difference: -0.0998659
Test for difference = 0 (vs > 0): Z = 0.28 P-Value = 0.388
Decision: 0.388 > 0.05 , so Fail to reject the null hypothesis
Conclusion: There exists sufficient evidence at the 5% level of significance that the true proportion of Denver women ages 21-29 with college degrees is more than the true proportion of Denver men ages 21-29 with college degrees.