Question

1 point) Independent random samples, each containing 60 observations, were selected from two populations. The samples from populations 1 and 2 produced 33 and 22 successes, respectively. Test H0:(p1−p2)=0 against Ha:(p1−p2)≠0. Use α=0.08.

(a) The test statistic is____

(b) The P-value is ____

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

Answer 1

We have given for the example              
              
x1=33          
n1=60          
              
x2=22          
n2=60          
Level of significance=   0.08          
Estimate for sample proportion 1=
              
Estimate for sample proportion 2=

              
Pooled proportion =
              
a)

Z test statistic for two proportions.


=2.02  

b) P value is = 0.0439.............................by using Z table or by using =2*(1-NORMSDIST(2.02))

P value is 0.0439 < 0.08

(c)  A. We can reject the null hypothesis that (p1−p2)=0 and accept that (p1−p2)≠0.