From 88 of its restaurants, Noodles & Company managers collected data on per-per

Question

From 88 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?

The hypothesis for the given issue is H0: Percentage of Sales and Per-Person Spending are independent.

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.)

From 88 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?

Explanation / Answer

a) Correct answer is Yes.

The statistical software outut for this problem is:

Contingency table results:
Rows: var3
Columns: None

Chi-Square test:

Hence,

Test statistic = 22.14

DF = 4

p - value = 0.0002

c) Yes, we reject the null and find dependence.

Low Medium High Total Low 12 14 3 29 Medium 12 11 3 26 High 11 4 18 33 Total 35 29 24 88

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