The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: "Do you think sexual harassment is a major problem in the American workplace?" Some 24% of the men compared to 62% of the women responded "Yes." Suppose that 150 women and 200 men were interviewed. What is the value of the test statistic?

Question

Quizplus · Accepted Answer

To determine whether there is a significant difference in perception of sexual harassment on the job between men and women, we can use a two-sample z-test for proportions. Let p1 be the proportion of women who believe sexual harassment is a major problem in the workplace, and p2 be the proportion of men who believe the same. The null hypothesis is that the two proportions are equal (p1 = p2), and the alternative hypothesis is that they are not equal (p1 ≠ p2).

The test statistic can be calculated using the formula:
z = (p1 - p2) / sqrt{ p*(1-p) * [ (1/n1) + (1/n2) ] }
where p = (x1 + x2) / (n1 + n2), and x1 and x2 are the number of women and men who answered "Yes," respectively.

Plugging in the given values, we get:
p1 = 0.62, p2 = 0.24, n1 = 150, n2 = 200
p = (150+200) / (150+200) = 0.3571
z = (0.62 - 0.24) / sqrt{ 0.3571*(1-0.3571) * [ (1/150) + (1/200) ] } = 7.173

The critical value at a 5% significance level for a two-tailed test with degrees of freedom (df) = n1 + n2 - 2 = 348 is approximately ±1.96. Since 7.173 > 1.96, we reject the null hypothesis and conclude that there is a significant difference in perception of sexual harassment on the job between men and women.

The Wall Street Journal Recently Ran an Article Indicating Differences