Question

A market researcher believes that brand perception of one of the company’s products may vary between different groups. After interviewing 343 persons, the following data was compiled. Can we conclude that brand perception is dependent on age?

Age                        Favorable            Unfavorable       Neutral

18-30                     57                           16                           17          

30-45                     78                           24                           27          

Over 45                 76                           24                           24          

b. State the null and the alternate hypotheses.

c. State the degrees of freedom and the critical value – use the chi-square chart and a 0.05 level of significance.

d. Use your calculator to determine the test statistic and the p-value.

e. Conclude the test by comparing the test statistic and the critical value.

f. Conclude the test by comparing the p-value and the level of significance.

g. State your conclusion IN CONTEXT.

Answer 1

b) Ho: brand perception is independent on age

Ha: brand perception is dependent on age

c)

Level of Significance =   0.05
Number of Rows =   3
Number of Columns =   3
Degrees of Freedom=(#row - 1)(#column -1) = (3- 1 ) * ( 3- 1 ) =   4

Critical Value =   9.488   [ Excel function: =CHISQ.INV.RT(α,DF) ]  

d)

Chi-Square Test of independence
	Observed Frequencies
	F	U	N				Total
18-30	57	16	17				90
30-45	78	24	27				129
>45	76	24	24				124
Total	211	64	68				343
	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	F	U	N				Total
18-30	211*90/343=55.364	64*90/343=16.793	68*90/343=17.843				90
30-45	211*129/343=79.356	64*129/343=24.07	68*129/343=25.574				129
>45	211*124/343=76.28	64*124/343=23.137	68*124/343=24.583				124
Total	211	64	68				343
(fo-fe)^2/fe	F	U	N				total
18-30	0.048	0.037	0.040				0.1256
30-45	0.023	0.000	0.079				0.103
>45	0.001	0.032	0.014				0.2284

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   0.275

e)) Decision: test statistic,X² < critical value , So, Do not reject the null hypothesis  

f)

p-Value =   0.9913   [Excel function: =CHISQ.DIST.RT(χ²,df) ]  
Decision:    p value > α , do not reject Ho      

g)

There is no evidence to conclude that  brand perception is dependent on age