In a survey of working parents (both parents working), one of the questions asked was "Have you refused a job, promotion, or transfer because it would mean less time with your family?" Two hundred men and 200 women were asked this question. Twenty-nine percent of the men and 24% of the women responded “yes." a. Based on this survey, can we conclude that there is a difference in the proportion of man and women responding “yes" at the 0.05 level of significance? (i) State the null and alternative hypotheses (ii) What test statistics would you use and why? (iii) Compute the value of the test-statistic. (iv) What rejection region would you use? (v) State your conclusion in the context of the problem.

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In a survey of working parents (both parents working), one of the questions asked was
"Have you refused a job, promotion, or transfer because it would mean less time with
your family?" Two hundred men and 200 women were asked this question. Twenty-nine percent
of the men and 24% of the women responded "yes."
a. Based on this survey, can we conclude that there is a difference in the proportion of man and
women responding “yes" at the 0.05 level of significance?
(i) State the null and alternative hypotheses
(ii) What test statistics would you use and why?
(iii) Compute the value of the test-statistic.
(iv) What rejection region would you use?
(v) State your conclusion in the context of the problem.
b. What P-value is associated with this test? Based on this P-value, could H. be rejected at
significance level 0.08?
c. Find a 95% confidence interval for the difference between the proportion of men and women
responding "yes." Based on this confidence interval, would your conclusion be the same as in
part a? Give reason(s) to support your answer.
Transcribed Image Text:In a survey of working parents (both parents working), one of the questions asked was "Have you refused a job, promotion, or transfer because it would mean less time with your family?" Two hundred men and 200 women were asked this question. Twenty-nine percent of the men and 24% of the women responded "yes." a. Based on this survey, can we conclude that there is a difference in the proportion of man and women responding “yes" at the 0.05 level of significance? (i) State the null and alternative hypotheses (ii) What test statistics would you use and why? (iii) Compute the value of the test-statistic. (iv) What rejection region would you use? (v) State your conclusion in the context of the problem. b. What P-value is associated with this test? Based on this P-value, could H. be rejected at significance level 0.08? c. Find a 95% confidence interval for the difference between the proportion of men and women responding "yes." Based on this confidence interval, would your conclusion be the same as in part a? Give reason(s) to support your answer.
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