Competition in the personal computer market is intense A sam

Competition in the personal computer market is intense. A sample of 450 purchases showed 202 Brand A computers, 175 Brand B computers, and 73 other computers. Use a .05 level of significance to test the null hypothesis that Brand A and Brand B have the same share of the personal computer market. What is p-value?

Solution

Formulating the hypotheses          
Ho: pA^ - pB^   =   0  
Ha: pA^ - pB^   =/=   0  

Here, we see that pdo =    0   , the hypothesized population proportion difference.  
          
Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.448888889      
p2 = x2/n2 =    0.388888889      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.032830947      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    1.827544015      
          
As significance level =    0.05   , then the critical z is  
          
zcrit =    1.959963985      
          
Also, the p value is          
          
P =    0.067618015   [ANSWER, P VALUE]
          
As p > 0.05, then we    FAIL TO REJECT THE NULL HYPOTHESIS.

There is no significant evidence that Brand A and Brand B do NOT have the same share of the personal computer market.   [conclusion]