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 Australia.Of those sampled,11 of the men and 19 of the women did believe that sexual discrimination is a problem.
- What is the value of the test statistic?
A) Z = -1.20
B) Z = -1.05
C) Z = -0.85
D) Z = -2.55

Question

Quizplus · Accepted Answer

We can use the two sample proportion test formula to calculate the test statistic:

Z = (p1 - p2) / sqrt( p * (1 - p) * ((1/n1) + (1/n2)))

where
p1 = proportion of men who believe sexual discrimination is a problem = 11/50 = 0.22
p2 = proportion of women who believe sexual discrimination is a problem = 19/40 = 0.475
p = overall proportion = (11 + 19) / (50 + 40) = 0.3
n1 = sample size of group 1 (men) = 50
n2 = sample size of group 2 (women) = 40

Substituting these values, we get:

Z = (0.22 - 0.475) / sqrt(0.3 * (1 - 0.3) * ((1/50) + (1/40)))
Z = -2.55

Therefore, the value of the test statistic is -2.55, which corresponds to option D.

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