From 77 of its restaurants, Noodles & Company managers collected data on per-per

Question

From 77 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 = .01, is per-person spending independent of percent of sales from potstickers? Potsticker % of Sales Per Person Spending Low Medium High Row Total Low 11 4 8 23 Medium 6 11 6 23 High 4 13 14 31 Col Total 21 28 28 77 PictureClick here for the Excel Data File (a) The hypothesis for the given issue is H0: 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 "0" wherever required.) Test statistic d.f. p-value (c) We reject the null and find dependence. Yes No

Explanation / Answer

Sample size = 77

H0: Percentage of Sales and Per-Person Spending are independent.

Ha : Percentage of Sales and Per-Person Spending are not independent.

Observed Table:

Expected Table

Chi - square statistic

degree of freedom = (3-1) * (3-1) = 4 chi- square statistic X2 = 10.64

alpha = 0.01

X20.01 = 13.2767

p - value = 0.030955

so here X2 < X20.01 so we shall not reject the null hypothesis and can conclude that Percentage of Sales and Per-Person Spending are independent.

Low Medium High Total Low 11 6 4 21 Medium 4 11 13 28 High 8 6 14 28 Total 23 23 31 77

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