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.	3,188	19.75%
Jif	28	1,857	8.80
Jif	40	730	5.48
Peter Pan	10	4,056	16.47
Skippy	18	6,221	28.16
Skippy	28	1,665	12.23
Skippy	40	1,468	9.11
Total		19,185

Goodness-of-Fit Test
	obs	expected	O – E	(O – E)2/E	% of chisq
	3,188	3,789.038	-601.038	95.340	11.47
	1,857	1,688.280	168.720	16.861	2.03
	730	1,051.338	-321.338	98.216	11.82
	4,056	3,159.770	896.230	254.205	30.58
	6,221	5,402.496	818.504	124.007	14.92
	1,665	2,346.326	-681.326	197.843	23.80
	1,468	1,747.754	-279.754	44.779	5.39
	19,185	19,185.002	-.002	831.251	100.01

(a) Show that it is appropriate to carry out a chi-square test and calculate the value of the test statistic. (Round your answers χ2 to 2 decimal places and χ2.05 to 3 decimal places.)

Each expected value is ≥                

χ2χ2
χ2.05χ.052

(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 α = .05.

(Click to select)  Reject  Do not reject   H₀. Conclude purchase behavior is  (Click to select)  not consistent  consistent  .

Answer 1

Answer: 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.

Solution:

The given results from the table:

Each expected value is ≥ 5

Test statistic, χ2 = 831.25

At α = 0.05

df = (r-1)(c-1) = (7 - 1)(2 - 1) = 6

Critical value of χ2 at α = 0.05 and df = 6

Critical value of χ2 = 12.592

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

α = .05.

The hypothesis test:

Null hypothesis, Ho: The purchase behavior of the panel of 2,500 households is consistent with the purchase behavior of the population of all peanut butter purchasers.  

Alternative hypothesis, Ha: The purchase behavior of the panel of 2,500 households is not consistent with the purchase behavior of the population of all peanut butter purchasers.  

Since, test statistic χ2 (831.25) > Critical value of χ2 (12.592).

We reject the null hypothesis, Ho.

There is sufficient evidence to conclude that purchase behaviour is not consistent.