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 = - 0.85
C)Z = - 1.05
D)Z = - 1.20

Question

Quizplus · Accepted Answer

To test if there is a significant difference between the proportions of men and women who believe that sexual discrimination is a problem, we can use a two-sample z-test for proportions.

The null hypothesis is that the proportion of men who believe sexual discrimination is a problem is equal to the proportion of women who believe the same. The alternative hypothesis is that the proportion of women who believe sexual discrimination is a problem is significantly higher than the proportion of men.

Let p1 be the proportion of men who believe sexual discrimination is a problem, and p2 be the proportion of women who believe the same. The sample proportion for group 1 is p̂1 = 11/50 = 0.22, and the sample proportion for group 2 is p̂2 = 19/40 = 0.475.

The combined sample proportion is p̂c = (11 + 19)/(50 + 40) = 0.3. The standard error of the difference in proportions is:

SE = sqrt{ p̂c(1-p̂c) [1/50 + 1/40] } = 0.118

The test statistic is:

z = (p̂1 - p̂2) / SE = (-0.255) / 0.118 = -2.16

Using a standard normal distribution table, the p-value for a two-tailed test is 0.0314. This means that the probability of observing a difference in proportions as extreme as the one in our sample, assuming the null hypothesis is true, is 0.0314.

Since this p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is evidence of a significant difference in attitudes about sexual discrimination between men and women.

The closest choice to our test statistic is A)Z = - 2.55, which is within the margin of error due to rounding. Therefore, the best choice is A.

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