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. 3,165 20.10% Jif 28 1,892 10.10 Jif 40 726 5.42 Peter Pan 10 4,079 16.01 Skippy 18 6,206 28.56 Skippy 28 1,627 12.33 Skippy 40 1,420 7.48 Total 19,115 Goodness-of-Fit Test obs expected O – E (O – E)2/E % of chisq 3165 3842.115 –677.115 119.331 13.56 1892 1930.615 –38.615 0.772 0.09 726 1036.033 –310.033 92.777 10.54 4079 3060.312 1018.689 339.092 38.52 6206 5459.244 746.756 102.147 11.60 1627 2356.880 –729.880 226.029 25.68 1420 1429.802 –9.802 0.067 0.01 19115 19115.000 0.000 880.216 100.00 (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. Assume here that purchase decisions by panel members are reasonably independent, and set α = .05. (Round your answers x2 to 2 decimal places and x2.05 to 3 decimal places.)

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. 3,165 20.10% Jif 28 1,892 10.10 Jif 40 726 5.42 Peter Pan 10 4,079 16.01 Skippy 18 6,206 28.56 Skippy 28 1,627 12.33 Skippy 40 1,420 7.48 Total 19,115 Goodness-of-Fit Test obs expected O – E (O – E)2/E % of chisq 3165 3842.115 –677.115 119.331 13.56 1892 1930.615 –38.615 0.772 0.09 726 1036.033 –310.033 92.777 10.54 4079 3060.312 1018.689 339.092 38.52 6206 5459.244 746.756 102.147 11.60 1627 2356.880 –729.880 226.029 25.68 1420 1429.802 –9.802 0.067 0.01 19115 19115.000 0.000 880.216 100.00 (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. Assume here that purchase decisions by panel members are reasonably independent, and set α = .05. (Round your answers x2 to 2 decimal places and x2.05 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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Question

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.	3,165	20.10%
Jif	28	1,892	10.10
Jif	40	726	5.42
Peter Pan	10	4,079	16.01
Skippy	18	6,206	28.56
Skippy	28	1,627	12.33
Skippy	40	1,420	7.48

Total		19,115

Goodness-of-Fit Test
	obs	expected	O – E	(O – E)²/E	% of chisq
	3165	3842.115	–677.115	119.331	13.56
	1892	1930.615	–38.615	0.772	0.09
	726	1036.033	–310.033	92.777	10.54
	4079	3060.312	1018.689	339.092	38.52
	6206	5459.244	746.756	102.147	11.60
	1627	2356.880	–729.880	226.029	25.68
	1420	1429.802	–9.802	0.067	0.01

	19115	19115.000	0.000	880.216	100.00

(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. Assume here that purchase decisions by panel members are reasonably independent, and set α = .05. (Round your answers x² to 2 decimal places and x².05 to 3 decimal places.)


χ2

Expert Solution

Step 1

Given information:

Brand	Observed	Market share
Jif 18 oz	3165	20.1%
Jif 28 oz	1892	10.1%
Jif 40 oz	726	5.42%
Petern Pan 10 oz	4079	16.01%
Skippy 18 oz	6206	28.56%
Skippy 28 oz	1627	12.33%
Skippy 40 oz	1420	7.48%
Sum	19115	100%

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