I know the answer is B because we have to pool the data. But I'm looking for an explanation of why we have to pool it.  Why do we do it sometimes and not others?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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I know the answer is B because we have to pool the data. But I'm looking for an explanation of why we have to pool it.  Why do we do it sometimes and not others?

5. An SRS of 45 male employees at a large company found that 36 felt that the company was supportive
of female and minority employees. An independent SRS of 40 female employees found that 24 felt that
the company was supportive of female and minority employees. Let p, represent the proportion of all
male employees at the company and p, represent the proportion of all female employees members at the
company who hold this opinion. We wish to test the hypotheses H,: p, - p, = 0 vs. H: p, - p, <0. Which of
the following is the correct expression for the test statistic?
(A)
0.8 -0.6
(0.8)(0.2) (0.6)(0.4)
+
45
40
(B)
0.8-0.6
(0.706)(0.294) , (0.706)(0.294)
45
40
(C)
0.8-0.6
(0.706)(0.294) (0.706)(0.294)
45
40
(D)
0.8-0.6
(0.8)(0.2) , (0.6)(0.4)
V45
V40
(E)
0.8
0.6
(0.8)(0.2) ' (0.6)(0.4)
J45
V40
Transcribed Image Text:5. An SRS of 45 male employees at a large company found that 36 felt that the company was supportive of female and minority employees. An independent SRS of 40 female employees found that 24 felt that the company was supportive of female and minority employees. Let p, represent the proportion of all male employees at the company and p, represent the proportion of all female employees members at the company who hold this opinion. We wish to test the hypotheses H,: p, - p, = 0 vs. H: p, - p, <0. Which of the following is the correct expression for the test statistic? (A) 0.8 -0.6 (0.8)(0.2) (0.6)(0.4) + 45 40 (B) 0.8-0.6 (0.706)(0.294) , (0.706)(0.294) 45 40 (C) 0.8-0.6 (0.706)(0.294) (0.706)(0.294) 45 40 (D) 0.8-0.6 (0.8)(0.2) , (0.6)(0.4) V45 V40 (E) 0.8 0.6 (0.8)(0.2) ' (0.6)(0.4) J45 V40
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