In 2003, Major League Baseball took steps to speed up the paly of baseball games

Question

In 2003, Major League Baseball took steps to speed up the paly of baseball games in order to maintain fan interest. In a sample of 89 games in 2002, 39 finished in less than 3 hours. A similar survey in 2003 of 83 games found that 44 finished in less than 3 hours. When testing the hypothesis (at the 5% level of significance) a higher percentage of games finished in less than 3 hours in 2003, what is the test statistic? (please round your answer to 2 decimal places)

Here's how I think to answer:

39/89 = .44

44/83= .53

v.44(1-.44)/89 + .53(1-.53)/83 = .0759

(.44-.53) / .0759= 1.19

??????????? Am I on the right track??????

2.57

1.21 ± 2%

Here's how I think to answer:

39/89 = .44

44/83= .53

v.44(1-.44)/89 + .53(1-.53)/83 = .0759

(.44-.53) / .0759= 1.19

??????????? Am I on the right track??????

Explanation / Answer

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 =    0.530120482      
p2 = x2/n2 =    0.438202247      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.075942061      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    1.210373192   [ANSWER]  

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