From 75 of its restaurants, Noodles & Company managers collected data on per-per

Question

From 75 of its restaurants, Noodles & Company managers collected data on per-person sales and the percent of sales due to “potstickers” (a popular food item). Both numerical variables failed tests for normality, so they tried a chi-square test. Each variable was converted into ordinal categories (low, medium, high) using cutoff points that produced roughly equal group sizes. At = 0.01, is per-person spending independent of percent of sales from potstickers?

Potsticker % of Sales Per person Spending Low Medium High Row Total Low   14 6 3 23 Medium   16 7 5 28 High   15 5 4 24 Col Total 45 18 12 75

Explanation / Answer

Doing an Expected Value Chart,          
          
13.8   5.52   3.68  
16.8   6.72   4.48  
14.4   5.76   3.84  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    0.412353347      
          
With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,          
          
a =    3      
b =    3      
          
df =    4      
          
Thus, the critical value is          
          
significance level =    0.01      
          
chi^2(critical) =    13.27670414      
          
As chi^2 < 13.277, then we fail to reject Ho.

There is no significant evidence that per-person spending is dependent of percent of sales from potstickers. [CONCLUSION]

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