Question

M7: Non-Parametric Techniques Scenario Assignment
Caption: Princess Foods Corporation has observed the changing awareness of the population on health and
nutrition. Therefore, they want to investigate the acceptance of a low-calorie product and a low-sodium product
by market segment.(gender) Are people more concerned about low-calorie soups or low-sodium soups and
how does that break down by market segment (age)?
Mieke: Here’s what we did: Two hundred customers were selected at random for two different interviews. We
were hoping that the information that we gleaned from these interviews would indicate the relative interest in
low-calorie and/or low-sodium soup and how that interest was broken down by market segment. That’s going
to give us insight into what the market wants and insight into who this customer is.

Assignment

The question that was asked, “Which of the following three products are you most interested in?” Then the
results were tallied, indicating how many males and how many females preferred each of the three options. A
study for each collected the following data. Test for independence at a significance of 5%.
1) What are your conclusions and how would you recommend the results be used by the marketing
department?

Categories	Male	Female
Low calorie	12	46
Regular broth	22	32
Creamed soup	66	22

2) A second question that was asked, “Which of the following three products are you most interested in?” Then
the results were tallied, indicating by age category preference for each of the three options. A study for each
collected the following data. Test for independence at a significance of 5%.

Categories	50 years or younger	Over 50
Low sodium	31	40
Regular broth	33	38
Creamed soups	36	22

Please provide step by step calculations and walk through in Excel when solving the problem

Answer 1

Answers :

1)

Hypothesis :

H0 : Gender and Low calorie products preference are Independent

H1 : Gender and Low calorie products preference are Dependent

As per below Chi-square calculations,

Chi-square statistic = 43.78

Chi-square critical value = 5.991 ( degrees of freedom = 2 and alpha = 0.05 ) [ As per below Chi-square table]

Since Chi-square statistic = 43.78 > Chi-square critical value = 5.991

Conclusion : Reject Ho.

Hence it is concluded that "Gender and Low calorie products preference are Dependent"

For Marketing dept.

i) More proportion of Females prefer Low calorie and Regular broth as compared with Males.

ii) More proportion of Males prefer Creamed soup as compared with Females.

I. Observed counts
	Male	Female	Column Total (CT)
Low calorie	12	46	58
Regular broth	22	32	54
Creamed soup	66	22	88
Row Total (RT)	100	100	200	GT
II. Expected counts = (RT x CT ) /GT
Expected frequency (E)	Male	Female	Total
Low calorie	29.00	29.00	58
Regular broth	27.00	27.00	54
Creamed soup	44.00	44.00	88
Total	100	100	200
III. Chi-square components
Chi-square calculations	Male	Female	Total
Low calorie	9.97	9.97	19.93
Regular broth	0.93	0.93	1.85
Creamed soup	11.00	11.00	22.00
Total	21.89	21.89	43.78	<== Chi-square value

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2.

Hypothesis :

H0 : Age and Low calorie products preference are Independent

H1 : Age and Low calorie products preference are Dependent

As per below Chi-square calculations,

Chi-square statistic = 4.87

Chi-square critical value = 5.991 ( degrees of freedom = 2 and alpha = 0.05 ) [ As per below Chi-square table]

Since Chi-square statistic = 4.87 < Chi-square critical value = 5.991

Conclusion : Accept Ho.

Hence it is concluded that "Age and Low calorie products preference are Independent"

I. Observed counts
	50 years or younger	Over 50	Column Total (CT)
Low calorie	31	40	71
Regular broth	33	38	71
Creamed soup	36	22	58
Row Total (RT)	100	100	200	GT
II. Expected counts = (RT x CT ) /GT
Expected frequency (E)	50 years or younger	Over 50	Total
Low calorie	35.50	35.50	71
Regular broth	35.50	35.50	71
Creamed soup	29.00	29.00	58
Total	100	100	200
III. Chi-square components
Chi-square calculations	50 years or younger	Over 50	Total
Low calorie	0.57	0.57	1.14
Regular broth	0.18	0.18	0.35
Creamed soup	1.69	1.69	3.38
Total	2.44	2.44	4.87	<== Chi-square value

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