STAT 400 Lecture AL1 Examples for 9 2 The 2 Test of Homogeneity Spring 2015 Dalpiaz one margin fixed Independent random samples from r populations Each sample classified in c response categories H 0 In each response category the probabilities are equal for all r populations The 2 Test of Independence neither margin fixed A random sample of size n is simultaneously classified with respect to two characteristics one has r categories and the other c categories H 0 The two classifications are independent that is each cell probability is the product of the row and column marginal probabilities Test Statistic Q cells O E 2 E O observed cell frequency E row total column total grand total Rejection Region 2 Reject H 0 if Q d f No of rows 1 No of columns 1 r 1 c 1 1 We wish to test whether the proportions of individuals with each of the four blood types are the same in two neighboring towns Town X and Town Y A random sample of 300individuals from Town X and 200 individuals from Town Y produced the following observed frequencies Blood Type O A B AB Town X 120 85 60 35 300 Town Y 100 45 30 25 200 220 130 90 60 500 Use 0 05 to test H 0 p XO p YO p XA p YA p XB p YB p XAB p YAB 2 In a random sample of 500 voters each individual was asked whether he or she thought inflation of unemployment was a more serious problem The individuals were also classified by party affiliation The results were as follows Party Unemployment Inflation Democrat 150 70 Republican 100 80 Other 60 40 Use a 5 level of significance and test whether political party affiliation and perceived problem are independent 3 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 We wish to test whether drug A and drug B have the same cure rate H 0 p AC p BC p AN p BN Recall p 1 p Y1 n1 78 0 65 120 p 2 Y2 n2 111 0 74 150 Y1 Y 2 78 111 189 0 70 n 1 n 2 120 150 270 Test Statistic Z 0 65 0 74 1 1 0 70 0 30 120 150 1 60357
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