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 p-value for a two-tailed test?
A).3849
B).1151
C).2301
D).3453

Question

Quizplus · Accepted Answer

To calculate the p-value for a two-tailed test, we need to calculate the z-score first using the formula

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

where 
p1 = proportion of female workers who favored the change = 28/50 = 0.56
p2 = proportion of male workers who favored the change = 22/50 = 0.44
p = pooled proportion = (p1 * n1 + p2 * n2) / (n1 + n2) = (28 + 22) / (50 + 50) = 0.5
n1 = sample size of female workers = 50
n2 = sample size of male workers = 50

Putting these values in the formula, we get:

z = (0.56 - 0.44) / sqrt (0.5 * (1-0.5) * (1/50 + 1/50)) = 1.3856

The p-value for a two-tailed test can be calculated using a z-table or a calculator, and it turns out to be 0.2301. Therefore, the correct answer is option C.

A New Policy of "Flex Hours" Is Proposed