Use the following scenario to answer questions 8 12 A recent

Use the following scenario to answer questions 8- 12. A recent article about the university graduates in the United States reports that in 2000, 52% of all graduates in the United States were female, whereas, in 1995, their percentage was only 44%. Suppose these data are based on a random sample of 200 graduates in 1995 (n1), and the 2000 data are also based on a random sample of 200 graduates (n2). Did the percentage of females graduates change over time? Assume a=0.05

What is the correct calculated value of the statistical test?

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 =    0.52      
p2 = x2/n2 =    0.44      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.036834766      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    2.171861214   [ANSWER, TEST STATISTIC]

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Further information:  
          
As significance level =    0.05   , then the critical z is  
          
zcrit =    1.959963985      
          
Also, the p value is          
          
P =    0.029866133      
          
Thus comparing z and zcrit (or p and significance level), then we    REJECT THE NULL HYPOTHESIS.