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

My Answer:

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.