In the book Business Research Methods (5th ed.), Donald R. Cooper and C. William

Question

In the book Business Research Methods (5th ed.), Donald R. Cooper and C. William Emory discuss a market researcher for an automaker who is studying consumer preferences for styling features of larger sedans. Buyers, who were classified as “first-time” buyers or “repeat” buyers, were asked to express their preference for one of two types of styling—European styling or Japanese styling. Of 40 first-time buyers, 9 preferred European styling and 31 preferred Japanese styling. Of 60 repeat buyers, 39 preferred European styling, and 21 preferred Japanese styling.

Test the hypothesis that buyer status (repeat versus first-time) and styling preference are independent at the .05 level of significance. What do you conclude? (Round your answer to 3 decimal places.)

In the book Business Research Methods (5th ed.), Donald R. Cooper and C. William Emory discuss a market researcher for an automaker who is studying consumer preferences for styling features of larger sedans. Buyers, who were classified as “first-time” buyers or “repeat” buyers, were asked to express their preference for one of two types of styling—European styling or Japanese styling. Of 40 first-time buyers, 9 preferred European styling and 31 preferred Japanese styling. Of 60 repeat buyers, 39 preferred European styling, and 21 preferred Japanese styling.

Explanation / Answer

b)

Doing an Expected Value Chart,          
          
19.2   20.8  
28.8   31.2  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    17.36778846   [ANSWER, chi^2 test statistic]

****************************************  
          
Other info:

With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,          
          
a =    2      
b =    2      
          
df =    1      
          
Thus, the critical value is          
          
significance level =    0.05      
          
chi^2(critical) =    3.841458821      
          
Also, the p value is          
          
P =    3.08002*10^-5      
          
As chi^2 > 3.841, and P < 0.05,, we   REJECT THE NULL HYPOTHESIS.      
          
Thus, there is significant evidence that buyer status (repeat versus first-time) and styling preference are NOT independent at the .05 level of significance. [CONCLUSION]

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