Question

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.

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%

What are your conclusions and how would you recommend the results be used by the marketing department? Please show in detail how to solve this in excel.

Categories	Male	Female
Low Calorie	12	46
Regular Broth	22	32
Creamed Soups	66	22

Answer 1

Solution:

Here, we have to use chi square test for independence of two categorical variables.

Null hypothesis: H0: Two variables are independent.

Alternative hypothesis: Ha: Two variables are dependent.

We assume level of significance = α = 0.05

Test statistic formula is given as below:

Chi square = ∑[(O – E)^2/E]

Where, O is observed frequencies and E is expected frequencies.

E = row total * column total / Grand total

We are given

Number of rows = r = 3

Number of columns = c = 2

Degrees of freedom = df = (r – 1)*(c – 1) = 2*1= 2

α = 0.05

Critical value = 5.99146455

(by using Chi square table or excel)

Calculation tables for test statistic are given as below:

Observed Frequencies
	Gender
Categories	Male	Female	Total
Low sodium	12	46	58
Regular Broth	22	32	54
Creamed Soups	66	22	88
Total	100	100	200

Expected Frequencies
	Gender
Categories	Male	Female	Total
Low sodium	29	29	58
Regular Broth	27	27	54
Creamed Soups	44	44	88
Total	100	100	200

Calculations
(O - E)
-17	17
-5	5
22	-22

(O - E)^2/E
9.965517	9.965517
0.925926	0.925926
11	11

Test Statistic = Chi square = ∑[(O – E)^2/E] = 43.7828863

χ2 statistic = 43.7828863

P-value = 0.0000

(By using Chi square table or excel)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the two variables gender and product categories are dependent.