In a survey of families in which both parents work, one of the questions asked w
ID: 3177403 • Letter: I
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 25% of the men and 28% 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. (Give your answer correct to two decimal places.)
(ii) Find the p-value. (Give your answer correct to four decimal places.)
Explanation / Answer
Solution:-
pmen = 0.25, nmen = 200
pwomen = 0.28, nwomen = 200
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: Pmen = Pwomen
Alternative hypothesis: Pmen Pwomen
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the proportion from population 1 is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a two-proportion z-test.
Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).
p = (p1 * n1 + p2 * n2) / (n1 + n2)
p = 0.265
S.E = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
S.E = 0.04413
z = (p1 - p2) / SE
z = - 0.68
where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.
Since we have a two-tailed test, the P-value is the probability that the z-score is less than - 0.68 or greater than 0.68.
Thus, the P-value = 0.4966
Interpret results. Since the P-value (0.4966) is greater than the significance level (0.05), we have to accept the null hypothesis.
From the above test we do not have sufficient evidence that there is a difference in the proportion of men and women responding "yes" at the 0.05 level of significance.
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