In an experiment on the effectiveness of music on the willingness of customers to spend money in a supermarket, researchers selected 400 customers at random. Some of the customers shopped on days when the supermarket did not play background music. The other group of customers shopped on days in which the supermarket broadcast music and advertising. Each customer was put into one of three groups—high, medium, and low willingness to spend—based on the total sum of purchases.

(a) Determine the empirical chi-square value so that the chi-square test is not biased.

(b) Can we conclude from the data with an error probability of α ¼ 5% that there is a connection between music and the total purchase sum?

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With music (x = 1) Without music (x = 2) Sum (Y) Number (exp. frequencies) Number (exp. frequency) Number High expenditures (y = 1) 130 (89.25) 40 (80.75) 170 Middle expenditures (y = 2) 30 (26.25) 20 (23.75) 50 Low expenditures (y = 3) 50 (94.50) 130 (85.50) 180 Sum (X) 210 190 400