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. -2.721 c. -2.431 d. -3.364 e. -1.040

Solution

Test Statistic
Sample 1 : X1 =200, n1 =400, P1= X1/n1=0.5
Sample 2 : X2 =109, n2 =200, P2= X2/n2=0.545
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.515
Q^ Value For Proportion= 1-P^=0.485
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.5-0.545)/Sqrt((0.515*0.485(1/400+1/200))
Zo =-1.04

Ans) e. -1.040