The publisher of a sports magazine plans to offer new subscribers one of three g

Question

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 also with the logo of their favorite team. In a sample of 560 new subscribers, the number selecting each gift is reported below. At the 0.02 significance level, is there a preference for the gifts or should we conclude that the gifts are equally well liked? (Negative amounts should be indicated by a minus sign. Round 2 value to 4 decimal places. Leave no cells blank - be certain to enter "0" wherever required. Round "fe" and "f0 - fe" to 2 decimal places and (f0 - fe)2/fe to 4 decimal places.)

. There a preference for the gifts.

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 also with the logo of their favorite team. In a sample of 560 new subscribers, the number selecting each gift is reported below. At the 0.02 significance level, is there a preference for the gifts or should we conclude that the gifts are equally well liked? (Negative amounts should be indicated by a minus sign. Round 2 value to 4 decimal places. Leave no cells blank - be certain to enter "0" wherever required. Round "fe" and "f0 - fe" to 2 decimal places and (f0 - fe)2/fe to 4 decimal places.)

Explanation / Answer

1) Set up the null hypothesis and alternative hypothesis.

Ho: The gifts are equally liked

H1: The gifts are not equally liked

2) State the decision rule.

DF = 2, significance level=0.02

So, from chi square table, CV = 7.824

Reject Ho if chi-square >7.824

3) calculations for the test statistic.

        x² = [(fo - fe )² / fe ]

gift

fo

fe

fo-fe

(fo-fe)2/fe

sweatshirt

180

186.6667

-6.66667

0.23809524

coffee cup

190

186.6667

3.333333

0.05952381

earrings

190

186.6667

3.333333

0.05952381

Total

560

560

0

0.35714

So X2 is 0.35714

So we fail to reject Ho

gift

fo

fe

fo-fe

(fo-fe)2/fe

sweatshirt

180

186.6667

-6.66667

0.23809524

coffee cup

190

186.6667

3.333333

0.05952381

earrings

190

186.6667

3.333333

0.05952381

Total

560

560

0

0.35714

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