Question

A market researcher believes that brand perception of one of the company's products may vary between different groups. After interviewing 373 persons, the following data was compiled. Can we conclude that brand perception is dependent on age? Age Favorable Unfavorable Neutral Total 18-30 80 27 25 132 30-45 73 27 23 123 Over 45 69 25 24 118 Total 222 79 72 373

Step 1 of 8: State the null and alternative hypothesis.
H0:brand perception and age are dependant, Ha: brand perception and age are independent OR H0:brand perception and age are independent, Ha:brand perception and age are dependant

Step 2 of 8: Find the expected value for the number of particpants who are 1818-3030 years old and have a favorable perception of the brand. Round your answer to one decimal place.

Step 3 of 8: Find the expected value for the number of particpants who are 3030-4545 years old and have a favorable perception of the brand. Round your answer to one decimal place.

Step 4 of 8: Find the value of the test statistic. Round your answer to three decimal places.

Step 5 of 8: Find the degrees of freedom associated with the test statistic for this problem.

Step 6 of 8: Find the critical value of the test at the 0.0250.025 level of significance. Round your answer to three decimal places.

Step 7 of 8: Make the decision to reject or fail to reject the null hypothesis at the 0.0250.025 level of significance.
Fail to reject Null hypothesis OR Reject Null hypothesis

Step 8 of 8: State the conclusion of the hypothesis test at the 0.0250.025 level of significance.

Answer 1

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	Unfavorable	favorable	nuetral	Total
	18-30	78.563	27.957	25.480	132
	30-45	73.206	26.051	23.743	123
	over 45	70.231	24.992	22.777	118
	total	222	79	72	373
chi square    χ2	=(Oi-Ei)2/Ei	Unfavorable	favorable	nuetral	Total
	18-30	0.0263	0.0328	0.0090	0.0681
	30-45	0.0006	0.0346	0.0232	0.0584
	over 45	0.0216	0.0000	0.0656	0.0872
	total	0.0484	0.0673	0.0979	0.2137
test statistic X2 =		0.214

step 1)

H0:brand perception and age are independent, Ha:brand perception and age are dependant

Step 2 of 8:  expected value =78.6

step 3: expected value =73.2

Step 4 of 8: \

test statistic X2 =

0.214

step 5:

degree of freedom(df) =(rows-1)*(columns-1)=

4

step 6:

for 4 df and 0.025 level , critical value       χ2=

11.143

step 7:

fail to reject the null

step 8:

we do not have sufficient evidence