A firm has the choice to pay a dividend or to reinvest its p

A firm has the choice to pay a dividend or to reinvest its profits. The firm decides to survey its shareholders and the following results are obtained concerning the number of shares owned and the shareholder\'s preference.

0-99

Test the investor\'s assumptions at the 5% level of significance.

Solution

Doing an Expected Value Chart,          
          
30   21   9  
30   21   9  
40   28   12  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    5.306349206      
          
With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,          
          
a =    3      
b =    3      
          
df =    4      
          
Thus, the critical value is          
          
significance level =    0.05      
          
chi^2(critical) =    9.487729037      
          
Also, the p value is          
          
P =    0.257283148      
          
Thus, comparing chi^2 and chi^2(crit) [or, p and significance level], we   FAIL TO REJECT THE NULL HYPOTHESIS.      
          
Thus, there is no significant evidence that the number of shares owned and the shareholder\'s preference are dependent to each other. [CONCLUSION]