Question

Based on information from Harper's Index, 37 out of a random sample of 100 adult Americans who did not attend college believe in extraterrestrials. However, out of a random sample of 100 Americans who did attend college, 41 claim that they believe in extraterrestrials. At the 1% significance level, does this indicate that the proportion of people who attended college who believe in extraterrestrials is higher than the proportion who did not attend college?

Answer 1

Try a z-test for proportions (two samples).

Here is one such formula:

z = (p1 - p2)/(√pq)[√(1/n1 + 1/n2)]

p1 = 41/100 = .41
p2 = 37/100 = .37
p = (x1 + x2)/(n1 + n2) = (41 + 37)/(100 + 100) = 78/200 = .39
q = 1 - p = 1 - .39 = .61

Substitute into the formula:

z = (.41 - .37)/[√(.39)(.61)][√(1/100 + 1/100) = .58 (rounded)

Testing at the 1% significance level for a one-tailed test, you will fail to reject the null. You cannot conclude a difference.

Double check these calculations.
I hope this helps.