The publisher of a sports magazine plans to offer new subscribers one of three gifts: a sweatshirt with the logo of their favorite team, a coffee cup with the logo of their favorite team, or a pair of earrings with the logo of their favorite team. In a sample of 519 new subscribers, the number selecting each gift is reported below. At the 0.05 significance level, is there a preference for the gifts or should we conclude that the gifts are equally well liked?
| Gift | Frequency |
| Sweatshirt | 190 |
| Coffee cup | 148 |
| Earrings | 181 |
a) State the decision rule. Use 0.05 significance level
b) How many degrees of freedom are there?
c) Compute the value of chi-square
|
d) What is your decision regarding H0
a)
| degree of freedom =categories-1= | 2 | |||
| for 0.05 level and 2 df :crtiical value X2 = | 5.9915 | |||
| Decision rule: reject Ho if value of test statistic X2>5.991 | ||||
b)
| degree of freedom =categories-1= | 2 | |||
c)
| applying chi square goodness of fit test: |
| observed | Expected | residual | Chi square | ||
| category | foi | fe | fo-fei | (fOi-fEi)2/fEi | |
| sweatshirt | 190.0 | 173.00 | 17.00 | 1.6705 | |
| cofee cup | 148.0 | 173.00 | -25.00 | 3.6127 | |
| earnings | 181.0 | 173.00 | 8.00 | 0.3699 | |
| total | 519 | 519 | 5.6532 | ||
| test statistic X2 = | 5.6532 | ||||
d)
fail to reject Ho
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