Page 735 10. A magazine publisher is testing four different covers for her anniv
ID: 3297305 • Letter: P
Question
Page 735
10. A magazine publisher is testing four different covers for her anniversary issue and wants to know if each one appeals equally to people of both genders. Fifty subjects are brought in, and each selects the cover that would most draw him or her to buy the magazine. The number of people of each gender who chose each cover is shown in the following table:
Gender of Subject Cover I Cover II Cover III Cover IV
Female 12 10 5 3
Male 5 9 1 5
10a. Test the null hypothesis ( = .05) that cover preference is indepdendent of gender.
10b. If you reject the null hypothesis in part a, test the preferences of each gender separately (i.e., perform two one-way chi-square tests) to see if the preferences are equal within each gender. If you did not reject the null hypothesis in part a, ignore gender (i.e., sum the frequencies for each cover for the two genders) and perform a one-way chi-square test to see if the four covers are equally preferred.
Explanation / Answer
Ans:
Chi square test:
a) H0:Cover prefrence is independent of gender.
H1:Cover preference is not independent of the gender.
Test statistic:
Calculated chi square score=4.273
df=(2-1)*(4-1)=3
p-value =CHIDIST(4.273,3)=0.2335
As,p-value>0.05,We fail to reject null hypothesis.
There is sufficient evidence to conclude that cover preference is indepdendent of gender.
b)Now,sum up the frequencies for both genders and test the equal prefernce forfour covers.
H0:four covers are equally preferred.
H1:four covers are not equally preferred.
Test statistic:
Calculated chi square score=10
df=4-1=3
p-value=CHIDIST(10,3)=0.0186
As,p-value<0.05,Reject null hypothesis.
There is sufficient evidence to conclude that four covers are not equally preferred.
Observed(O) Cover I Cover II Cover III Cover IV Total Female 12 10 5 3 30 Male 5 9 1 5 20 Total 17 19 6 8 50 Expected(E) Cover I Cover II Cover III Cover IV Total Female 10.2 11.4 3.6 4.8 30 Male 6.80 7.60 2.40 3.20 20 Total 17 19 6 8 50 Chi square=(O-E)^2/E Cover I Cover II Cover III Cover IV Female 0.318 0.172 0.544 0.675 Male 0.476 0.258 0.817 1.013 Total Chi square score=4.273Related Questions
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