For the given table of observed frequencies perform a test f

For the given table of observed frequencies, perform a test for independence, using the a = 0.01 level of significance. A. Do not reject H0. B. Reject H0.

Solution

Doing an Expected Value Chart,          
          
58.63570392   71.40783745   69.95645864  
81.21044993   98.89985486   96.88969521  
62.15384615   75.69230769   74.15384615  

          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    14.06859651      
          
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 =    0.01      
          
chi^2(critical) =    13.27670414      
          
Also, the p value is          
          
P =    0.007079312      
          
Thus, comparing chi^2 and chi^2(crit) [or, p and significance level], we   REJECT THE NULL HYPOTHESIS. [OPTION B]