Question

Q 6       A STUDY WAS CONDUCTED TO DETERMINE IF THERE IS A SIGNIFICANT RELATIONSHIP BETWEEN THE FREQUENCY OF MEAT SERVED AS A MAIN MEAL PER MONTH FOR INDIVIDUALS LIVING IN THE FOUR SECTIONS OF THE UNITED STATES. A QUESTIONAIRE WAS ADMINISTERED TO A RANDOM SAMPLE OF 400 FAMILIES AND THE RESULTS ARE SUMMARIZED BELOW                              
                                      
                                      
                                      
                                      
           FREQUENCY OF MEAT AS A MAIN MEAL PER MONTH                          
       LIVING AREA   LESS THAN 11   11 TO 20   MORE THAN 20   ROW TOTALS              
       EASTERN   46   36   20   102              
       SOUTH    40   40   26   106              
       WESTERN    16   38   38   92              
       NORTH   25   36   39   100              
       COLUMN TOTALS   127   150   123   400              
                                      
       DO THESE SAMPLE RESULTS INDICATE THAT THERE IS A SIFNIFICANT RELATIONSHIP BETWEEN THE FREQUENCY OF MEAT SERVED AS A MAIN MEAL PER MONTH AND GEOGRAPHIC LIVING AT ALPHA = 0.01                              
                                      
                                      

Answer 1

First we compute the expected frequency for each of the 12 cells here as:
Ei = (Sum of column i)*(Sum of row i) / Grand Total

These are computed in the circular brackets below as:

The chi square test statistic contribution here is computed as:

These are given in the square bracket in the given table.

These are summed to obtain the chi square test statistic here as:

Degrees of freedom here is computed as:
Df = (num of rows - 1)*(Num of columns - 1) = (4 - 1)*(3 - 1) = 6

Therefore the p-value is now obtained from the chi square distribution tables here as:

As the p-value here is 0.000235 < 0.01 which is the level of significance, therefore the test is significant here and we can reject the null hypothesis here. Therefore we have sufficient evidence here that the two variables are associated here that is not independent.