A new policy of "flex hours" is proposed. Random sampling showed that 28 of 50 female workers favored the change, while 22 of 50 male workers favored the change. Management wonders if there is a difference between the two groups. What is the test statistic to test for a zero difference in the population proportions?
A)1.321
B)1.287
C)1.200
D)-1.255

Question

Quizplus · Accepted Answer

To test for a zero difference in the population proportions, we can use the two-sample z-test for proportions.

The formula for the test statistic is:
z = (p1 - p2) / sqrt(p * (1-p) * (1/n1 + 1/n2))
where p is the pooled proportion, n1 and n2 are the sample sizes, and p1 and p2 are the sample proportions for each group.

In this case, we have:
n1 = n2 = 50
p1 = 28/50 = 0.56
p2 = 22/50 = 0.44
p = (28 + 22) / (50 + 50) = 0.5

Substituting these values into the formula, we get:
z = (0.56 - 0.44) / sqrt(0.5 * 0.5 * (1/50 + 1/50)) = 1.2

Therefore, the test statistic is 1.2, which corresponds to choice C.

A New Policy of "Flex Hours" Is Proposed