Construct the indicated confidence interval for thedifference between population

Question

Construct the indicated confidence interval for thedifference between population proportionsp1-p2Assume that the samples are independent andthat they have been randomly selected.

x1 = 61, n1 = 105 andx2 = 82, n2 = 120; Construct a 98% confidenceinterval for the difference between population proportionsp1 - p2.



a. 0.432 < p1 -p2 < 0.730

b. 0.456 <p1 - p2 < 0.707

c. -0.228 <p1 - p2 < 0.707

d. -0.252 <p1 - p2 < 0.047 Construct the indicated confidence interval for thedifference between population proportionsp1-p2Assume that the samples are independent andthat they have been randomly selected.

x1 = 61, n1 = 105 andx2 = 82, n2 = 120; Construct a 98% confidenceinterval for the difference between population proportionsp1 - p2.



a. 0.432 < p1 -p2 < 0.730

b. 0.456 <p1 - p2 < 0.707

c. -0.228 <p1 - p2 < 0.707

d. -0.252 <p1 - p2 < 0.047

Explanation / Answer

Given x1 = 61, n1 = 105, p1=61/105=0.581    x2 = 82, n2= 120, p2=82/120=0.683 =0.02, |Z(0.01)|=2.326 (check normal table) The 98% CI is (p1-p2) ± Z*[p1*(1-p1)/n1]+[p2*(1-p2)/n2] --> (0.581-0.683) ± 2.326*sqrt(0.581*(1-0.581)/105 +0.683*(1-0.683)/120) --> ( -0.251,   0.047) Answer: d. -0.252

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