Question

Given two independent random samples with the following results:

n1=122	n2=329
x1=43	x2=89

Can it be concluded that there is a difference between the two population proportions? Use a significance level of α=0.1α=0.1 for the test.

Step 5 of 6 :  

Find the P-value for the hypothesis test. Round your answer to four decimal places.

CORRECT ANSWER: P= 0.0930

CORRECT ANSWER: P= 0.0930

CORRECT ANSWER: P= 0.0930

CORRECT ANSWER: P= 0.0930

CORRECT ANSWER: P= 0.0930

Answer 1

Ho:   p1 - p2 =   0          
Ha:   p1 - p2 ╪   0          
                  
sample #1   ----->              
first sample size,     n1=   122          
number of successes, sample 1 =     x1=   43          
proportion success of sample 1 , p̂1=   x1/n1=   0.3524590          
                  
sample #2   ----->              
second sample size,     n2 =    329          
number of successes, sample 2 =     x2 =    89          
proportion success of sample 1 , p̂ 2=   x2/n2 =    0.270517          
                  
difference in sample proportions, p̂1 - p̂2 =     0.3525   -   0.2705   =   0.0819
                  
pooled proportion , p =   (x1+x2)/(n1+n2)=   0.2926829          
                  
std error ,SE =    =SQRT(p*(1-p)*(1/n1+ 1/n2)=   0.04823          
Z-statistic = (p̂1 - p̂2)/SE = (   0.082   /   0.0482   ) =   1.6990
                  
  
p-value =        0.0891 ≈0.0930 [excel formula =2*NORMSDIST(-z)]      
decision :    p-value<α,Reject null hypothesis               
it can be concluded that there is a difference between the two population proportions