Question

In a survey of families in which both parents work, one of the questions asked was, "Have you refused a job, promotion, or transfer because it would mean less time with your family?" A total of 200 men and 200 women were asked this question. "Yes" was the response given by 26% of the men and 22% of the women. Based on this survey, can we conclude that there is a difference in the proportion of men and women responding "yes" at the 0.05 level of significance? (Use Men − Women.)

(a) Find z. (Round your answer to two decimal places.)


Find the p-value. (Round your answer to four decimal places.)


(b) State the appropriate conclusion.

Fail to reject the null hypothesis. There is not significant evidence that the proportions differ. Reject the null hypothesis. There is not significant evidence that the proportions differ.     Fail to reject the null hypothesis. There is significant evidence that the proportions differ. Reject the null hypothesis. There is significant evidence that the proportions differ.

Answer 1

H0: p1 = p2

Ha: p1 p2

This is two tailed test

Pooled proportion = [ (1 * n1 + 2 * n2 ) / ( n1 + n2 ) ]  

= [ ( 200 * 0.26 + 200 * 0.22) / (200 + 200) ]

= 0.24

a)

Test statistics

z = (​​​​​​1 - 2) / sqrt [ ( 1 - ) * ( 1 / n1 + 1/n2 )]

= ( 0.26 - 0.22) / sqrt [ 0.24 ( 1 - 0.24) * ( 1 / 200 + 1 / 200) ]

= 0.94

p-value = 2 * P(Z > z)

= 2 * P(Z > 0.94)

= 2 * 0.1736

= 0.3472

b)

Since p-value > 0.05 level, we fail to reject H0.

Conclusion - Fail to reject the null hypothesis. There is not significant evidence that the proportions differ