Question

Based on information from a previous study, r1 = 40 people out of a random sample of n1 = 98 adult Americans who did not attend college believe in extraterrestrials. However, out of a random sample of n2 = 98 adult Americans who did attend college, r2 = 49 claim that they believe in extraterrestrials. Does this indicate that the proportion of people who attended college and who believe in extraterrestrials is higher than the proportion who did not attend college? Use α = 0.01.

Answer 1

Z-test for the difference in proportions(one tailed):

Null Hypothesis(H0):

The proportion of people who attended college and who believe in extraterrestrials is not significantly higher than the proportion who did not attend college. P2 - P1 0.

Alternative Hypothesis(H1):

The proportion of people who attended college and who believe in extraterrestrials is significantly higher than the proportion who did not attend college. P2 - P1 > 0. (Right-tailed test).

Test statistic:

p1 =r1/n1 =40/98 =0.41

p2 =r2/n2 =49/98 =0.50

Pooled sample proportion, p =(r1+r2)/(n1+n2) =(40+49)/(98+98) =89/196 =0.4541

Standard Error, SE = = =0.0711

Test statistic, Z =(p2 - p1)/SE =(0.50 - 0.41)/0.0711 =1.27

Critical value of Z:

Significance level, =0.01; type of test =right-tailed. So, the critical value of Z is Z_crit =2.33

Conclusion:

Since the test statistic of 1.27 is less than the critical value of 2.33 (i.e., Z < Z_crit), we failed to reject the null hypothesis(H0) at 0.01 significance level. Thus, we do not have enough evidence to claim the alternative hypothesis.

So, it does not indicate that the proportion of people who attended college and who believe in extraterrestrials is higher than the proportion who did not attend college.