In a random sample of 120 male customers at Burger Queen 84

In a random sample of 120 male customers at Burger Queen, 84 ordered fries with their with their burgers.

a) Find the p-value of the test H 0 : p = 0.77 vs. H 1 : p 0.77, where p is the proportions of male customers who order fries with their burgers.

b) Suppose also that in a random sample of 80 female customers, 48 ordered fries with their burgers. Find the p-value of the test H 0 : p M = p F vs. H 1 : p M > p F .

Solution

a)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.77
Ha:   p   =/=   0.77
As we see, the hypothesized po =   0.77      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.7      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.038416576      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -1.8221301      
          
As this is a    2   tailed test, then, getting the p value,  
          
p =    0.068435247   [ANSWER]

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b)

Formulating the hypotheses          
Ho: p1^ - p2^   <=   0  
Ha: p1^ - p2^   >   0  
Here, we see that pdo =    0   , the hypothesized population proportion difference.  
          
Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.7      
p2 = x2/n2 =    0.6      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.068920244      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    1.4509525      
          
          
Also, the p value is, using the right tailed area,          
          
P =    0.073396544   [ANSWER]