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.If the p-value turns out to be 0.035 (which is not the real value in this data set), then
A)at = 0.05, you should fail to reject H₀
B)at = 0.04, you should reject H₀
C)at = 0.03, you should reject H₀
D)None of the above would be correct statements.

Question

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.If the p-value turns out to be 0.035 (which is not the real value in this data set), then
A)at = 0.05, you should fail to reject H₀ 
B)at = 0.04, you should reject H₀ 
C)at = 0.03, you should reject H₀ 
D)None of the above would be correct statements.

Quizplus · Accepted Answer

Assuming a significance level of 0.05, a p-value of 0.035 suggests that there is strong evidence against the null hypothesis (H₀) that there is no difference in attitudes towards sexual discrimination between men and women. Therefore, we should reject H₀ and conclude that there is a significant difference in attitudes between the two groups. The correct statement would be to reject H₀ at a significance level of 0.05, which is closest to the given p-value of 0.035. Choice B is the closest answer. Assuming a two-sided hypothesis test where the null hypothesis (H₀) is that men and women do not differ in their attitudes about sexual discrimination, and the alternative hypothesis (H₁) is that they do differ in their attitudes.

We can calculate the p-value using a two-sample proportions test.

The proportion of men who believe that sexual discrimination is a problem is 11/50 = 0.22. 
The proportion of women who believe that sexual discrimination is a problem is 19/40 = 0.475. 
The pooled proportion is (11+19)/(50+40) = 0.3225.

The standard error can be calculated as:

sqrt((0.3225*(1-0.3225)/50) + (0.3225*(1-0.3225)/40)) = 0.111

The test statistic can be calculated as:

(z = (0.475 - 0.22) / 0.111 = 2.306)

Looking at a standard normal distribution table, we find that the p-value for z = 2.306 is 0.0214.

Since 0.0214 is smaller than the given p-value of 0.035, we can reject the null hypothesis and conclude that there is evidence that men and women differ in their attitudes about sexual discrimination.

Thus, the best choice is B, which states that at a significance level of 0.04 (which is a smaller value than the given p-value of 0.035), we should reject H₀.

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