Question 8 Background: Job offer and Time with Family \"Have you ever refused a

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Question 8 Background: Job offer and Time with Family "Have you ever refused a job, promotion, or transfer because it would lead to spending less time with your family?" This question was asked in a survey of two independent random samples representing two populations: Population 1: all working adults living in the East with a family of at least two children Population 2: all working adults living in the Midwest with a family of at least two children The researcher would like to assess if the proportion of all such working adults living in the East who have refused a job for this reason would exceed the same proportion for all such working adults living in the Midwest. The significance level is set to 5%. The results of the study are summarized below. Number who have refused a job Sample Size Sample Proportion because less time with family East 93 27 0.2903 Midwest 88 16 0.1818 Question 8 Subquestions 8.a The researcher sets up the null hypothesis as Ho: p1 -p2. Select the appropriate alternative hypothesis. point (s) Ha: p1 not equal to p2 Ha: p1 p2 Ha: p1 p2 Saved 8.b It is important to understand what the various parameters in the hypotheses represent. Consider the following incorrect definition for the parameter p1 point(s) "p1 is the sample proportion of working adults from the East who have refused a job for this reason." Provide the two words to complete this statement: This definition would be correct if you replace the word with the word No answer entered. Click above to enter an answer. 8.c The test statistic is computed assuming the null hypothesis is true, that is, p1 p2-p. Which of the following is the best estimate of that common proportion p? point(s) 0.1085 0.23605 0.2376 0.4721

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P1 = P2

Alternative hypothesis: P1 > P2

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the proportion of women catching cold (p1) is sufficiently smaller than the proportion of men catching cold (p2).

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).

c) p = (p1 * n1 + p2 * n2) / (n1 + n2)

p = 0.2376

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }

S.E = 0.0633

z = (p1 - p2) / SE

z = 1.714

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 one-tailed test, the P-value is the probability that the z-score is more than 1.714. We use the Normal Distribution Calculator to find P(z > 1.714) = 0.0436

e) Thus, the P-value = 0.0436

Interpret results. Since the P-value (0.0436) is less than the significance level (0.05), we have to reject the null hypothesis.

f) From the above test we do not have sufficient evidence in the favor of the claim that proportion of all such working adults in the east who refused a job for a reason would exceed the same proportion for all such working adults living in the midwest.

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