A powerful women's group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. Find the value of the test statistic.
A) Z = - 2.55
B) Z = - 1.05
C) Z = - 1.20
D) Z = - 0.85

Question

Quizplus · Accepted Answer

We can use a two-proportion z-test to compare the proportions of men and women who believe sexual discrimination is a problem. The null hypothesis is that the proportion of men and women who believe sexual discrimination is a problem is the same, and the alternative hypothesis is that they are different.

The test statistic is calculated as:
z = (p1 - p2) / sqrt(p * (1 - p) * (1/n1 + 1/n2))
where p1 and p2 are the sample proportions, p is the pooled proportion (calculated as (x1 + x2) / (n1 + n2)), n1 and n2 are the sample sizes, and x1 and x2 are the number of men and women who believe sexual discrimination is a problem.

Plugging in the values given, we get:
p1 = 11/50 = 0.22
p2 = 19/40 = 0.475
p = (11 + 19) / (50 + 40) = 0.3
n1 = 50
n2 = 40

z = (0.22 - 0.475) / sqrt(0.3 * 0.7 * (1/50 + 1/40)) = -2.546

Rounding to two decimal places, we get a test statistic of -2.55, which corresponds to choice A).

A Powerful Women's Group Has Claimed That Men and Women