A researcher is examining preferences among four new flavors

A researcher is examining preferences among four new flavors of ice cream. A sample of n = 100 people is obtained. Each person tastes all four flavors and then picks his/her favorite. The distribution of preferences is as follows.

                       Ice Cream Flavor

     A         B             C            D

   32

25

   30

13

Do these data indicate any significant preferences among the four flavors? Test at the .05 level of significance.

Solution

If there are no preferences, then each group must have 25.

Doing an observed/expected value table,          
O   E   (O - E)^2/E  
32   25   1.96  
25   25   0  
30   25   1  
13   25   5.76  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    8.72      
          
As df = a - 1,           
          
a =    4      
df = a - 1 =    3      
          
Then, the critical chi^2 value is          
          
significance level =    0.05      
chi^2(crit) =    7.814727903      
          
As chi^2 > 7.8147, we   REJECT THE NULL HYPOTHESIS.      
          
Thus, there is significant evidence that there are significant preferences among the four flavors. [CONCLUSION]