Independent random samples, each containing 800 observations, were selected from
ID: 3359576 • Letter: I
Question
Independent random samples, each containing 800 observations, were selected from two binomial populations. The samples from populations 1 and 2 produced 414 and 562 successes, respectively. (a) Test H0:(p1p2)=0H0:(p1p2)=0 against Ha:(p1p2)0Ha:(p1p2)0. Use =0.01=0.01 test statistic == rejection region |z|>|z|> The final conclusion is A. There is not sufficient evidence to reject the null hypothesis that (p1p2)=0(p1p2)=0. B. We can reject the null hypothesis that (p1p2)=0(p1p2)=0 and support that (p1p2)0(p1p2)0. (b) Test H0:(p1p2)0H0:(p1p2)0 against Ha:(p1p2)>0Ha:(p1p2)>0. Use =0.09=0.09 test statistic == rejection region z>z> The final conclustion is A. We can reject the null hypothesis that (p1p2)0(p1p2)0 and support that (p1p2)>0(p1p2)>0. B. There is not sufficient evidence to reject the null hypothesis that (p1p2)=0(p1p2)=0.
Explanation / Answer
Solution:
From the given information
p1= 414/800 = 0.5
p2= 562/800 = 0.7
(a) The test hypothesis is
Ho: (p1-p2) = 0
Ha: (p1-p2) 0
The test statistic is
Z = (p1-p2)/[(p1*(1-p1)/n1) +(p2*(1-p2)/n2)]
= (0.5-0.7)/sqrt(0.5*0.5/800 + 0.7*0.3/800)
= -8.3406
Given = 0.01, the critical value is Z(0.01) = -2.58 (check standard normal table)
Since Z =-8.3406 < -2.58, we reject Ho.
B. We can reject the null hypothesis that (p1p2)=0(p1p2)=0 and support that (p1p2)0(p1p2)0.
(b) The test hypothesis is
Ho: (p1-p2) 0
Ha: (p1-p2) > 0
The test statistic is
Z = (p1-p2)/[(p1*(1-p1)/n1) +(p2*(1-p2)/n2)]
= (0.5-0.7)/sqrt(0.5*0.5/800 + 0.7*0.3/800)
= -8.3406
Given = 0.01, the critical value is Z(0.09) = -1.695 (check standard normal table)
Since Z = -8.3406 < -1.695, we reject Ho.
A. We can reject the null hypothesis that (p1p2)0(p1p2)0 and support that (p1p2)>0(p1p2)>0.