Assume that you plan to use a significance level of alpha 0

Assume that you plan to use a significance level of alpha = 0.05 to test the claim that p1 = p2. Use the given sample sizes and numbers of successes to find the z test statistic for the hypothesis test. A random sampling of sixty pitchers from the National League and fifty-two pitchers from the American League showed that 19 National and 11 American League pitchers had E.R.A\'s below 3.5.

z = 1.629

z = 1.253

z = 191.183

z = 15.457

Solution

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 =    0.316666667      
p2 = x2/n2 =    0.211538462      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.082546837      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    1.253 [ANSWER, OPTION B]