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. Brand Size Number of Purchases by Household Panel Market Shares Jif 18 oz. 3,170 19.30% Jif 28 1,812 9.46 Jif 40 703 4.34 Peter Pan 10 4,079 18.36 Skippy 18 6,250 26.55 Skippy 28 1,670 13.77 Skippy 40 1,406 8.22 Total 19,090 Goodness-of-Fit Test obs expected O – E (O – E)2/E % of chisq 3,170 3,684.370 -514.370 71.811 8.68 1,812 1,805.914 6.086 .021 .00 703 828.506 -125.506 19.012 2.30 4,079 3,504.924 574.076 94.029 11.37 6,250 5,068.395 1,181.605 275.470 33.31 1,670 2,628.693 -958.693 349.638 42.28 1,406 1,569.198 -163.198 16.973 2.05 19,090 19,090.000 -0.000 826.954 99.99 (a) Show that it is appropriate to carry out a chi-square test. (b) 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. Use the Excel output of an appropriate chi-square test in the table below. Assume here that purchase decisions by panel members are reasonably independent, and set α = .05. (Round your answers χ2 to 2 decimal places and χ2.05 to 3 decimal places.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.

Brand	Size	Number of Purchases by Household Panel	Market Shares
Jif	18 oz.	3,170	19.30%
Jif	28	1,812	9.46
Jif	40	703	4.34
Peter Pan	10	4,079	18.36
Skippy	18	6,250	26.55
Skippy	28	1,670	13.77
Skippy	40	1,406	8.22
Total		19,090

Goodness-of-Fit Test
	obs	expected	O – E	(O – E)²/E	% of chisq
	3,170	3,684.370	-514.370	71.811	8.68
	1,812	1,805.914	6.086	.021	.00
	703	828.506	-125.506	19.012	2.30
	4,079	3,504.924	574.076	94.029	11.37
	6,250	5,068.395	1,181.605	275.470	33.31
	1,670	2,628.693	-958.693	349.638	42.28
	1,406	1,569.198	-163.198	16.973	2.05
	19,090	19,090.000	-0.000	826.954	99.99

(a) Show that it is appropriate to carry out a chi-square test.

(b) 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. Use the Excel output of an appropriate chi-square test in the table below. Assume here that purchase decisions by panel members are reasonably independent, and set α = .05. (Round your answers χ² to 2 decimal places and χ².05 to 3 decimal places.)

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