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. Assuming W designates women's responses and M designates men's, which of the following are the appropriate null and alternative hypotheses to test the group's claim?

a. H0: πM - πW ≤​ 0 versus H1: ​πM - πW > 0
b. H0: πM - πW ≥ 0 versus H1: ​πM- πW < 0
c. H0: πM - πW = 0 versus H1: ​πM - πW ≠​ 0
d. H0: πM - πW ≠ 0 versus H1: ​πM - πW = 0

Answer 1

c. H0: πM - πW = 0 versus H1: ​πM - πW ≠​ 0

Explanation:

Hello!

The women's group claims that men's and women's opinions about sexual discrimination are different.

A survey was conducted to test this claim, two groups where surveyed, group 1: n₁=50 men, group 2: n₂= 40 over their opinion whether sexual discrimination is a problem. The number of people that consider it a problem was recorded in both groups.

To test this claim you need to compare the proportions of people that consider sexual discrimination a problem for both groups, the hypothesis test to conduct is two-tailed, = vs. ≠

The correct answer is c.

Remember, in the null hypothesis H₀ the "no change situation" is stated, so it always carries the = symbol.

I hope this helps!