STAT 400 Lecture AL1 Examples for 7.3, 8.3 (Part 2) Spring 2015 Dalpiaz Consider two dichotomous populations, with “success” proportions p 1 and p 2 , respectively. Consider the sample proportions 111 ˆnxp = and 222 ˆnxp= where 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 ( ) 21ˆˆ pp − is approximately normal with mean p 1 – p 2 and standard deviation ( ) ( ) 222111 11nppnpp−⋅−⋅+. The confidence interval for the difference between two population proportions p 1 – p 2 is ( )( ) ( ) ˆˆˆˆ ˆˆ 222111221 11αnppnppzpp−⋅−⋅⋅+±− H 0 : p 1 = p 2 H 1 : p 1 < p 2 H 1 : p 1 > p 2 H 1 : p 1 ≠ p 2 Test Statistic: ( ) nnppppz=+−−⋅⋅ 21 21111 ˆˆˆˆ, where 2122112121 ˆˆˆnnpnpnnnxxp++=++=⋅⋅.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 78 111 Not cured 42 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
View Full Document
Unlocking...