In: Statistics and Probability
From 80 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
α = .05, is per-person spending independent of percent of
sales from potstickers?
Potsticker % of Sales | ||||||||||||
Per-Person Spending | Low | Medium | High | Row Total | ||||||||
Low | 17 | 10 | 5 | 32 | ||||||||
Medium | 9 | 13 | 4 | 26 | ||||||||
High | 4 | 4 | 14 | 22 | ||||||||
Col Total | 30 | 27 | 23 | 80 | ||||||||
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 "0" wherever required.)