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Question

You wish to test the following claim () at a significance level of .            

You obtain 163 successes in a sample of size 279 from the first population. You obtain 112 successes in a sample of size 235 from the second population.

question: What is the critical value for this test? critical value,  = 

Answer 1

The critical value would be the z-scores for 0.99 and 0.01: 2.33 and -2.33

sample 1 proportion phat1 = 163/279

sample 2 proportion phat2 = 112/235

the pooled sample proportion phat = (163 + 112)/(279 + 235)

the z-statistic for this test is (phat1-phat2)/sqrt(phat*(1-phat)(1/279 + 1/235):