Construct a 95% confidence interval for (p1 - p2) in each

Chapter 8, Problem 46E

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QUESTION:

Problem 46E

Construct a 95% confidence interval for (p1 - p2) in each of the following situations:

a. n1 = 400, 1 = .65; n2 = 400, 2 = .58

b. n1 = 180, 1 = .31; n2 = 250, 2 = .25

c. n1 = 100, 1 = .46; n2 = 120, 2 = .61

Questions & Answers

QUESTION:

Problem 46E

Construct a 95% confidence interval for (p1 - p2) in each of the following situations:

a. n1 = 400, 1 = .65; n2 = 400, 2 = .58

b. n1 = 180, 1 = .31; n2 = 250, 2 = .25

c. n1 = 100, 1 = .46; n2 = 120, 2 = .61

ANSWER:

Step 1 of 4

Large-sample 100(1-?)% confidence Interval for (P_1-P_2)(P_1-P_2):

 

  (\hat{p}_{1}-\hat{p}_{2})\pm Z_{\frac{\alpha }{2}}\sigma _{(\hat{p}_{1}-\hat{p}_{2})}= (\hat{p}_{1}-\hat{p}_{2})\pm Z_{\frac{\alpha }{2}} \sqrt{\frac{{p}_{1}{q}_{1}}{n_{1}}+\frac{{p}_{2}{q}_{2}}{n_{2}}}

                                              \approx  (\hat{p}_{1}-\hat{p}_{2})\pm Z_{\frac{\alpha }{2}} \sqrt{\frac{{p}_{1}{q}_{1}}{n_{1}}+\frac{{p}_{2}{q}_{2}}{n_{2}}}

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