Question

A researcher has conducted a survey for Danone yogurt to understand what type of customers buy its products. Thus, in the survey, each respondent is asked if he is a Blue or White collar employee (that is if the respondents has an office job or not) and whether he buys the company’s yogurt or not. The results are shown in the following cross-tabulation table. Danone Yogurt Buyer Nonbuyer Total White Collar 152 8 160 Blue Collar 14 26 40 Total 166 34 200

Danone Yogurt
	Buyer	Nonbuyer	Total
White Collar	152	8	160
Blue Collar	14	26	40
Total	166	34	200

a.) Using the table and your calculations, give a clear example of a cross-tabulation cell, column total, row total, grand total, observed frequency cell, expected frequency cell. (2 points)

b.) What is the maximum Chi-Square value you must have, for you to say that there is a statistically significant relationship between the two variables, with 95% accuracy? (1 point)

c.) Is there any relationship between the two variables, type of responder and buyer type? (3 points)

d.) What is the managerial insight you derive from this analysis? (2 points)

Answer 1

Chi-Square Test of independence
	Observed Frequencies
	0
0	B	N					Total
WC	152	8					160
BC	14	26					40
Total	166	34					200
	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	B	N					Total
WC	166*160/200=132.8	34*160/200=27.2					160
BC	166*40/200=33.2	34*40/200=6.8					40
Total	166	34					200
	(fo-fe)^2/fe
WC	2.776	13.553
BC	11.104	54.212

B)

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =

81.644

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          
              
p-Value =   0.0000   [Excel function: =CHISQ.DIST.RT(χ²,df) ]      
Decision:    p-value < α , Reject Ho          

C)

YES, there is a relationship between the two variables, type of responder and buyer type

D)

Sale of danone yougurt depends upon whether the employee is white or blue collar.