In preparing a defense against a hostile takeover a firms ma

In preparing a defense against a hostile takeover, a firm’s management assesses the owners of both common and preferred stock with respect to their attitudes toward current management. Of 400 common stockholders, 200 reported being in favor of a change in management. A sample of 200 preferred stockholders found 109 in favor of a management change. The firm’s management is interested in finding evidence at the .05 significance level of a difference in the proportion of the two stockholder groups that favors the management change. Give the value of the test statistic suggested by the testing situation described above. a. -1.850 b. -2.431 c. -3.364 d. -1.040 e. -2.721

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 =    0.5      
p2 = x2/n2 =    0.545      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.043184198      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    -1.040 [ANSWER, D]