Question

Decide whether the normal sampling distribution can be used. If it can be​ used, test the claim about the difference between two population proportions p 1 and p 2 at the given level of significance alpha using the given sample statistics. Assume the sample statistics are from independent random samples. ​Claim: p 1equalsp 2​, alphaequals0.01 Sample​ statistics: x 1equals27​, n 1equals129 and x 2equals32​, n 2equals206 Can a normal sampling distribution be​ used?

Answer 1

as n1p1.n1(1-p1), n2p2, n2(1-p2) all are greater than 10 therefore  normal sampling distribution be​ used

as test statistic 1.26 does not fall in rejection region, we can not reject null hypothesis.

We do not have sufficient evidence to conclude that there is difference between two population proportions.