Question

Independent random samples, each containing 60 observations, were selected from two populations. The samples from populations 1 and 2 produced 37 and 30 successes, respectively.
Test H0:(p1−p2)=0 against Ha:(p1−p2)≠0. Use α=0.05.

(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 conclude that (p1−p2)≠0.
B. There is not sufficient evidence to reject the null hypothesis that (p1−p2)=0.

Answer 1

(a)

We have given for the example              
              
x1=37          
n1=60          
              
x2=30          
n2=60          
Level of significance=   0.05          
Estimate for sample proportion 1
              
Estimate for sample proportion 2
              
Pooled proportion
              
Z test statistic formula is

  

  
              
= 1.29  

Z test statistic =1.29
              
      
(b) P-value   =0.1982 ........................by using Excel command =2*(1-NORMSDIST(1.29)) or by using Z table.   
(c) Decision:   Do not reject   H0  

P value is 0.1982 > 0.05

B. There is not sufficient evidence to reject the null hypothesis that (p1−p2)=0.