In the Journal of Marketing Research (November 1996), Gupta studied the extent to which the purchase behavior of scanner panels is representative of overall brand preferences. A scanner panel is a sample of households whose purchase data are recorded when a magnetic identification card is presented at a store checkout. The table below gives peanut butter purchase data collected by the A. C. Nielson Company using a panel of 2,500 households in Sioux Falls, South Dakota. The data were collected over 102 weeks. The table also gives the market shares obtained by recording all peanut butter purchases at the same stores during the same period. Market Brand Size Number of Purchases by Household Panel Shares Jif 18 oz. 3,184 19.65% Jif 28 1,833 10.30 Jif 40 719 4.70 Peter Pan10 4,044 18.87 Skippy 18 6,247 28.21 Skippy 28 1,660 12.49 Skippy 40 1,432 5.78 Total 19,119 Goodness-of-Fit Test obs expected O-E 3,184 3,756.884 -572.884 1,833 1,969.257 -136.257 719 898.593 -179.593 4,044 3,607.755 436.245 6,247 5,393.470 853.530 1,660 2,387.963 -727.963 1,432 19,11 9 1,105.078 326.922 19,119.000 -.000 (O - E)2/E % of chisq 87.359 13.67 9.428 1.48 35.893 5.62 52.750 8.25 135.07 21.13 3 221.91 34.72 7 96.715 15.13 639.13 100.00 5 (a) Show that it is appropriate to carry out a chi-square test. Each expected value is (b) Test to determine whether the purchase behavior of the panel of 2,500 households is consistent with the purchase behavior of the population of all peanut butter purchasers. Assume here that purchase decisions by panel members are reasonably independent, and set = .05. (Round your answers 2 to 2 decimal places and 2.05 to 3 decimal places.) 2 2.05 (Click to select) ev: 11_18_2012 H0. Conclude purchase behavior is . (Click to select)