Question

A recent small-scale study surveyed 300 men and women to ask “What automobile is attractive to you?” and asked them to choose from the five options below. Results of the survey are presented in the table. Conduct a test at the alpha=0.01 level to ascertain whether there is a difference in the pattern of responses between men and women consumers. (45 Points)

Auto Brand	Men	Women
Ford F-150	10	40
Mini Cooper	0	60
Geo Metro	60	0
Hyundai Genesis	40	10
Cadillac ATS	40	40

Answer 1

Null hypothesis: Ho: there is no difference in the pattern of responses between men and women consumers.

Alternative hypothesis:Ha: there is a difference in the pattern of responses between men and women consumers.

degree of freedom(df) =(rows-1)*(columns-1)=	4
for 4 df and 0.01 level , critical value       χ2=	13.277
Decision rule : reject Ho if value of test statistic X2>13.277

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	Men	Women	Total
	Ford F-150	25.00	25.00	50
	Mini Cooper	30.00	30.00	60
	Geo Metro	30.00	30.00	60
	Hyundai Genesis	25.00	25.00	50
	Cadillac	40.00	40.00	80
	total	150	150	300
chi square    χ2	=(Oi-Ei)2/Ei	Men	Women	Total
	Ford F-150	9.0000	9.0000	18.0000
	Mini Cooper	30.0000	30.0000	60.0000
	Geo Metro	30.0000	30.0000	60.0000
	Hyundai Genesis	9.0000	9.0000	18.0000
	Cadillac	0.0000	0.0000	0.0000
	total	78.0000	78.0000	156.0000
test statistic X2 =	156.00

since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that there is a difference in the pattern of responses between men and women consumers.

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