Question

In a consumer study investigating preferences for a new packaging material for granola bars, with the objective of the test being the comparison between the new packaging material (Package A) and the current packaging material (B). A same-difference test was conducted using 180 randomly-selected consumers at a supermarket. Each consumer was presented with two samples, with the combinations being AA, AB, BA or BB. The following results were obtained. A worked example is in your text book (pg. 103)   (7 pts)

		Subject Received	Subject Received
		Matched Pair (AA, BB)	Unmatched Pair (AB,BA)	TOTAL
Subject Said	Same	65	32
	Different	25	58
	Total

Questions:

Question 1: When panelists were presented with the same sample, how many panelists said the samples were the same? (ie. they were correct):

Question 2: When panelists were presented with the different sample, how many panelists said the samples were the same? (ie. they were incorrect):

Question 3: What is the expected total for the “different” condition?

Question 4: What is the calculated value for the same/match condition?

Question 5: What is the calculated value for the different/unmatched condition?

Question 6: What is TOTAL calculated chi-square value?

Question 7: For p=0.05, what is our critical value (taken from Table 19-5)? (0.5 pts)

Question 8: Are there significant differences between these two packaging materials? (0.5 pts)

Answer 1

1) panelists said the samples were the same = 65

2) panelists said the samples were the same = 32

3)

Chi-Square Test of independence
	Observed Frequencies
	0
	matched pair	unmatched					Total
same	65	32					97
different	25	58					83
Total	90	90					180
	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	matched pair	unmatched					Total
same	90*97/180=48.5	90*97/180=48.5					97
different	90*83/180=41.5	90*83/180=41.5					83
Total	90	90					180
	(fo-fe)^2/fe
same	5.6134	5.6134
different	6.5602	6.5602

expected total for the “different” condition = 41.5+41.5 = 83

4) calculated value for the same/match condition = 5.6134

5) calculated value for the different/unmatched condition = 6.5602

6) total Chi square value=24.347

7)

Level of Significance =   0.05
Number of Rows =   2
Number of Columns =   2
Degrees of Freedom=(#row - 1)(#column -1) = (2- 1 ) * ( 2- 1 ) =   1

Critical Value =   3.8415

8)

Decision: test stat,X² > critical value , So, Reject the null hypothesis

yes, there significant differences between these two packaging materials