Question

(S 11.3) Independent random samples of sizes n1 = 204 and n2 = 208 were taken from two populations. In the first sample, 177 of the individuals met a certain criteria whereas in the second sample, 179 of the individuals met the same criteria.

Test the null hypothesis H0:p1=p2versus the alternative hypothesis HA:p1>p2.

Calculate the z test statistic, testing the null hypothesis that the population proportions are equal. _______________ Round your response to at least 2 decimal places.

  

What is the approximate value of the p-value? __________________ Round your response to at least 4 decimal places

Answer 1

p1(hat)=177/204=0.86765

n1=204

p2(hat)=179/208=0.86058

n2=208

here z test for comparing proportion will be used

claim

H0: p1=p2

Ha: p1>p2

pooled sample proportion is

p= 0.86407

standard error of the test:

SE= 0.03376

So test statistics will be

z= [p1(hat)-p2(hat)]/SE

z=(0.86765-0.86058)/0.0338

z= 0.20936

rounded z test =0.21

since this is lower tail test

p value= p(z<0.209365)=0.41708

rounded p-value=0.4171

......................

there are two methods to solve it , i have used pooled proportion

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