In: Statistics and Probability
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.
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 |
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. |