A researcher plans a study in which a crucial step is offeri

A researcher plans a study in which a crucial step is offering participants a food reward. It is important that the three food rewards be equal in appeal. Thus, a pre-study was designed in which participants were asked which of the rewards they preferred. Of the 60 participants, 16 preferred cupcakes, 26 preferred candy bars, and 18 favored dried apricots.
a) Conduct a Chi-Square Test for Goodness of Fit. (Use a .05 significance level and make
sure you show all 5 steps of the hypothesis test)
b) Use the results of the Chi-Square test to describe the appeal of the food rewards.

Solution

a)

Let the three rewards be groups 1, 2, 3, respectively, as they are in the problem.

Ho: There is no preference when it comes to rewards.

Ha: There is preference when it comes to rewards.

Doing an observed/expected value table,          
O   E   (O - E)^2/E  
16   20   0.8  
26   20   1.8  
18   20   0.2  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    2.8      
          
As df = a - 1,           
          
a =    3      
df = a - 1 =    2      
          
Then, the critical chi^2 value is          
          
significance level =    0.05      
chi^2(crit) =    5.991464547      
          
Also, the p value is          
          
p =    0.246596964      
          
Thus, comparing chi^2 < 5.991 [or, p > 0.05], we   FAIL TO REJECT THE NULL HYPOTHESIS.      

Thus, there is no significant evidence that there is a preference in rewards.

*************************************

b)

Thus, there is no significant evidence that there is a special preference between rewards. All these (cupcakes, candy bars, dried apricots) are just the same in appeal.