Question

Conduct the following test at the α=0.01 level of significance by determining ​(a) the null and alternative​ hypotheses, ​(b) the test​ statistic, and​ (c) the​ P-value. Assume that the samples were obtained independently using simple random sampling.

Test whether p1≠p2.

Sample data are

x1=28​, n1=254​, x2=36​,and n2=302.

​(a) Determine the null and alternative hypotheses. Choose the correct answer below.

A.

H0: p1=p2 versus H1: p1>p2

B.

H0: p1=p2 versus H1: p1<p2

C.

H0: p1=p2 versus H1: p1≠p2

D.

H0: p1=0 versus H1: p1=0

​(b) The test statistic z0 is __?__.

​(Round to two decimal places as​ needed.)

​(c) The​ P-value is __?__.

​(Round to three decimal places as​ needed.)

Test the null hypothesis. Choose the correct conclusion below.

A.

Reject the null hypothesis because there is not sufficient evidence to conclude that p1<p2.

B.

Reject the null hypothesis because there is sufficient evidence to conclude that p1≠p2.

C.

Do not reject the null hypothesis because there is not sufficient evidence to conclude that p1≠p2.

D.

Do not reject the null hypothesis because there is sufficient evidence to conclude that p1>p2.

Answer 1

(a)  

C.

H0: p1=p2 versus H1: p1≠p2

(b)

We have given for the example              
              
x1=   28          
n1=   254          
              
x2=   36          
n2=   302          
Level of significance=   0.01          
Estimate for sample proportion 1=
              
Estimate for sample proportion 2=

              
Pooled proportion =
              
Z test statistic for two proportions.

=-0.33      

Z test statistic value is =-0.33
              
          
              
(c)   
  
P-value   =0.741 .....................by using Excel command =2*NORMSDIST(-0.33) or by using Z table.

P value is 0.741>0.01

Therefore,
Decision:   Do not reject   H0      

C.

Do not reject the null hypothesis because there is not sufficient evidence to conclude that p1≠p2.