From 78 of its restaurants, Noodles & Company managers collected data on per-per
ID: 3316504 • Letter: F
Question
From 78 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 = .02, is per-person spending independent of percent of sales from potstickers?
From 78 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 = .02, is per-person spending independent of percent of sales from potstickers? Potsticker % of Sales Per Person Spending Low Medium High Medium High Row Total Low 7 6 7 26 7 16 31 20 26 32 Col Total 21 78 &Click; here for the Excel Data File (a) The hypothesis for the given issue is Ho: Percentage of Sales and Per-Person Spending are independent Yes No (b) Calculate the chi-square test statistic, degrees of freedom, and the p-value. (Round your test statistic value to 2 decimal places and p-value to 4 decimal places. Leave no cells blank - be certain to enter "O" wherever required.) Test statistic d.f. p-valueExplanation / Answer
Ans:
a)Yes.
b)Expected count=row sum*column sum/overall sum
Total chi square score=6.054
Test statistic=6.05
df=(3-1)*(3-1)=2*2=4
p-value=CHIDIST(6.05,4)=0.1954
(without rounding off test statistc,p-value=0.1951)
Observed(O) per person spend low medium high row total low 7 6 7 20 medium 5 13 8 26 high 9 7 16 32 col total 21 26 31 78 Expected(E) per person spend low medium high row total low 5.38 6.67 7.95 20 medium 7.00 8.67 10.33 26 high 8.62 10.67 12.72 32 col total 21 26 31 78 chi square=(O-E)^2/E per person spend low medium high low 0.485 0.067 0.113 medium 0.571 2.167 0.527 high 0.017 1.260 0.847Related Questions
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