The college is planning to add a food vender in the student

The college is planning to add a food vender in the student union and would like to know what type of food service the students would prefer. A sample of 120 students is obtained and each student is asked to select his/her preference from a coffee shop, a pizza place, or a hamburger grill. The resulting frequency data are as follows:

i. Coffee= 53 Pizza = 37 Hamburger = 30

b. Do the data indicate any significant preferences among the three types of food service? Test at the .05 level of significance.

c. A similar survey of the student population ten years ago found that a coffee shop was preferred by 20% of the students and pizza and hamburger were each preferred by 40% of the students. Do the data indicate a significant change in preferences during the past ten years. State the hypotheses and find the expected frequencies for the chi-square test.

Solution

B)

Doing an observed/expected value table,          
O   E   (O - E)^2/E  
53   33.33333333   11.60333333  
37   33.33333333   0.403333333  
30   33.33333333   0.333333333  

          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    12.34      
          
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 =    0.002091236      
          
Thus, comparing chi^2 and chi^2(crit) [or, p and significance level], we   REJECT THE NULL HYPOTHESIS.      
          
Thus, there is significant evidence that there are significant preferences among the three types of food service.

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c)

Doing an observed/expected value table,          
O   E   (O - E)^2/E  
53   24   35.04166667  
37   48   2.520833333  
30   48   6.75  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    44.3125      
          
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 =    2.38596E-10      
          
Thus, comparing chi^2 and chi^2(crit) [or, p and significance level], we   REJECT THE NULL HYPOTHESIS.      
          
Thus, there is significant evidence that there is a significant change in preferences during the past ten years.

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