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.

Number of Purchases by Household Panel	Market Shares
Jif	18 oz.	3,169	19.15%
Jif	28	1,870	10.71
Jif	40	749	5.16
Peter Pan	10	4,026	16.38
Skippy	18	6,238	27.45
Skippy	28	1,661	12.68
Skippy	40	1,443	8.47
Total		19,156

Goodness-of-Fit Test
	obs	expected	O – E	(O – E)2/E	% of chisq
	3,169	3,668.374	-499.374	67.980	8.11
	1,870	2,051.608	-181.608	16.076	1.92
	749	988.450	-239.450	58.006	6.92
	4,026	3,137.753	888.247	251.448	29.98
	6,238	5,258.322	979.678	182.524	21.76
	1,661	2,428.981	-767.981	242.816	28.95
	1,443	1,622.513	-179.513	19.861	2.37
	19,156	19,156.001	-.001	838.711	100.01

(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 ?²to 2 decimal places and ?².05 to 3 decimal places.)

Answer 1

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

Each expected value is ? 5

for continuity the expected value for each cell should be ? 5

(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 ?2to 2 decimal places and ?2.05 to 3 decimal places.)

since the calculated  ?2=sum((O-E)²/E)=838.71 with df=n-1=7-1=6

is more than the critical ?2(.05,6)=12.592 , so we reject the null hypothesis that households is consistent with the purchase behavior of the population of all peanut butter purchasers .