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 with the logo of their favorite team. In a sample of 507 new subscribers, the number selecting each gift is reported below. At the 0.01 significance level, is there a preference for the gifts or should we conclude that the gifts are equally well liked?

Gift	Frequency
Sweatshirt	159
Coffee cup	166
Earrings	182

State the decision rule. Use 0.01 significance level. (Round your answer to 3 decimal places.)

How many degrees of freedom are there?

Compute the value of chi-square. (Negative amounts should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round "f_e" and "f_o - f_e" to 2 decimal places and (f_o - f_e)²/f_e to 4 decimal places. Round χ² to 4 decimal places.)

Gift	fo	fe	fo − fe	(fo − fe)^2/fe
Sweatshirt
Coffee Cup
Earrings
Total	507	507	0

What is your decision regarding H₀?

Answer 1

Gift	Observed Frequency (fO)	fe = 0.3*fo	fo-fe	(fo − fe)^2/fe
Sweatshirt	159	152.10	6.90	0.3130
Coffee cup	166	152.10	13.90	1.2703
Earrings	182	152.10	29.90	5.8778
Total	507	Test statistic		7.4611

H₀: Gifts are equally liked

H₁: There is a preference for gifts

Degrees of freedom:df = k-1 = 3-1 = 2

Level of significance = 0.01

Critical value (Using Excel function CHISQ.INV.RT(probabllity,df)) = CHISQ.INV.RT(0.01,2) = 9.210

Decision rule: Reject H₀ if test statistic > 9.210

Test statistic = 7.4611

Decision: Since test statisitic is less than critcal value, we do not reject null hypothesis.

So, gifts are equally liked.