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.	3,197	19.06%
Jif	28	1,892	8.83
Jif	40	715	4.87
Peter Pan	10	4,065	18.04
Skippy	18	6,222	28.28
Skippy	28	1,693	13.49
Skippy	40	1,441	7.43
Total		19,225

Goodness-of-Fit Test
	obs	expected	O – E	(O – E)2/E	% of chisq
	3,197	3,664.285	-467.285	59.590	8.99
	1,892	1,697.568	194.432	22.269	3.36
	715	936.258	-221.258	52.288	7.89
	4,065	3,468.190	596.810	102.700	15.49
	6,222	5,436.830	785.170	113.392	17.10
	1,693	2,593.453	-900.453	312.639	47.16
	1,441	1,428.418	12.582	.111	.02
	19,225	19,225.002	-.002	662.989	100.01

(a) Show that it is appropriate to carry out a chi-square goodness of fit 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 α = .05. (Round your answers χ²to 2 decimal places and χ².05 to 3 decimal places.)

χ2χ2 statistic
χ2.05χ.052

(Click to select)RejectDo not reject H₀. Conclude purchase behavior is (Click to select)not consistentconsistent.
ev: 11_18_2012

Answer 1

(a) From the data, each expected value is 5, therefore it is appropriate to carry out a chi square goodness of fit test.

___________________________________________________________________

(b) The Hypothesis:

H0: There is no difference in the purchase behaviour of the 2 populations. The data is consistent.

Ha: There is a significant difference in the purchase behaviour of the 2 populations.The data is not considtent.

The Test Statistic: = 662.99

The Critical Value: , df = n - 1 = 6 is 12.592

The Decision: Since > , We Reject H0.

The Conclusion: The data is not consistent.