Question

n 1998, the Nabisco Company launched a “1000 Chips Challenge” advertising campaign in which it was claimed that every 18-ounce bag of their Chips Ahoy cookies contains 1000 chips (on average). A curious statistics student purchased 8 randomly selected bags of cookies and counted the chocolate chips. The data is given below:

1200 1019 1214 1087 1214 900 1200 825

a) The student concluded that the data was not normally distributed and wanted to use a Wilcoxon Signed-Rank test to test the company’s claim. What assumption is needed in this case?

b) Assuming the assumption in part a. is met, at the 1% significance level, do the data provide sufficient evidence to conclude that the average number of chocolate chips in a bag of Chips Ahoy cookies differs from 1000? Carry out the Wilcoxon Signed-Rank Test by hand.

Answer 1

a) Yes, the assumption is enough i.e. the data was not normally distributed

so we have to use Wilcoxon signed- Rank test

b) Given los be alpha = 1% = 0.01

H0: the average number of chocolate chips in a bag of Chips Ahoy cookies not differs from 1000

H1; the average number of chocolate chips in a bag of Chips Ahoy cookies differs from 1000

From the given data

S.No.	Samples(X)	x-1000	|X-1000|	Rank Ri	Positive Rank	Negative Rank
1	1200	200	200	5.5	5.5
2	1019	19	19	1	1
3	1214	214	214	7.5	7.5
4	1087	87	87	2	2
5	1214	214	214	7.5	7.5
6	900	-100	100	3		3
7	1200	200	200	5.5	5.5
8	825	-175	175	4		4
				Total:	29	7

Thus we conclude that  the average number of chocolate chips in a bag of Chips Ahoy cookies not differs from 1000