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Logged in as IMA MATHEMATICAL ASSOCIATION OF AMERICA webwork / math243spring-schmidt / 0b-ch23 comparing two proportions 3 Week 10b - Ch23 Comparing Two Proportions: Problem 3 Previous Problem List Neat samples, each containing 70 observations, were selected from two populations. The samples from (1 point) Independent random populations 1 and 2 produced 35 and 25 successes, respectively. Test Ho : (pi-P2) = 0 against H. :(ph-n)20. Use ?-009. (a) The test statistic is b) The P-value is (c) The final conclusion is A. There is not sufficient evidence to reject the null hypothesis that (Pi P)0 B. We can reject the null hypothesis that (p-p)-0 and accept that (p -P)0 Note: You can eam partial credit on this probiem Preview My Answers Submit Answers You have attempted this problem 0 times You have unlimited attempts remaining Email instructor

Explanation / Answer

p1 = 35/70 = 0.5

p2 = 25/70 = 0.357

The pooled sample proportion(P) = (p1 * n1 + p2 * n2)/(n1 + n2)

                                                      = (0.5 * 70 + 0.357 * 70)/(70 + 70)

                                                      = 0.4285

SE = sqrt(P(1 - P) * (1/n1 + 1/n2))

       = sqrt(0.4285(1 - 0.4285) * (1/70 + 1/70))

       = 0.0836

a) The test statistic z = (p1 - p2)/SE

                                  = (0.5 - 0.357)/0.0836

                                  = 1.71

b) P-value = 2 * P(Z > 1.71)

                 = 2 * (1 - P(Z < 1.71))

                = 2 * (1 - 0.9564)

               = 0.0872

c) As the P-value is less than the significance level (0.0872 < 0.09), so the null hypothesis is rejected.

Option - B is correct conclusion.

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