Question

Independent random samples, each containing 500 observations, were selected from two binomial populations. The samples from populations 1 and 2 produced 388 and 188 successes, respectively.
(a) Test H0:(p1−p2)=0 against Ha:(p1−p2)≠0. Use α=0.04

test statistic =
rejection region |z|>
The final conclusion is

A. There is not sufficient evidence to reject the null hypothesis that (p1−p2)=0.  
B. We can reject the null hypothesis that (p1−p2)=0 and support that (p1−p2)≠0.

(b) Test H0:(p1−p2)≤0 against Ha:(p1−p2)>0. Use α=0.03

test statistic =
rejection region z>
The final conclustion is

A. There is not sufficient evidence to reject the null hypothesis that (p1−p2)=0.  
B. We can reject the null hypothesis that (p1−p2)≤0 and support that (p1−p2)>0.

Answer 1

a)

from above test statsitic z=12.80

rejection region |z|> 2.054

The final conclusion is : B. We can reject the null hypothesis that (p1−p2)≤0 and support that (p1−p2)≠0.

b)

test statistic =12.80

rejection region z>1.88

B. We can reject the null hypothesis that (p1−p2)≤0 and support that (p1−p2)>0.