STAT 400 Lecture AL1 Spring 2015 Dalpiaz Examples for 7 3 8 3 Part 2 Consider two dichotomous populations with success proportions p 1 and p 2 respectively Consider the sample proportions p 1 where x1 n1 p 2 and x2 n2 n 1 and n 2 are the sample sizes and x 1 and x 2 are the numbers of successes in the two samples from populations 1 and 2 respectively If n 1 and n 2 are large then mean p 1 p 2 p 1 p 2 and standard deviation is approximately normal with p 1 1 p 1 p 2 1 p 2 n1 n2 The confidence interval for the difference between two population proportions p 1 p 2 is p 1 p 2 z 2 p 1 1 p 1 p 2 1 p 2 n1 n2 H1 p1 p2 H0 p1 p2 H1 p1 p2 H1 p1 p2 Test Statistic z p 1 p 2 p 1 p 1 n 1 n 1 2 where x x n p n p p 1 2 1 1 2 2 n1 n 2 n1 n 2 1 In a comparative study of two new drugs A and B 120 patients were treated with drug A and 150 patients with drug B and the following results were obtained Drug A Drug B Cured Not cured 78 42 111 39 Total 120 150 a Construct a 95 confidence interval for the difference in the cure rates of the two drugs b We wish to test whether drug B has a higher cure rate than drug A Find the p value of the appropriate test
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