Question

In what ways do advertisers in magazines use sexual imagery to appeal to youth? One study classified each of 1509 full-page or larger ads as "not sexual" or "sexual," according to the amount and style of the dress of the male or female model in the ad. The ads were also classified according to the target readership of the magazine. Here is the two-way table of counts.

	Magazine readership
Model dress	Women	Men	General interest	Total
Not sexual	355	507	244	1106
Sexual	214	92	97	403
Total	569	599	341	1509

(A) Perform the significance test that compares the model dress for the three categories of magazine readership. Summarize the results of your test and give your conclusion. (Use α = 0.01. Round your value for χ² to two decimal places, and round your P-value to four decimal places.)

χ2 =
P-value =

(B) Conclusion, choose the best answer from the options below

Reject the null hypothesis. There is not significant evidence of an association between target audience and model dress.

Fail to reject the null hypothesis. There is not significant evidence of an association between target audience and model dress.   

Fail to reject the null hypothesis. There is significant evidence of an association between target audience and model dress.

Reject the null hypothesis. There is significant evidence of an association between target audience and model dress.

(C) All of the ads were taken from the March, July, and November issues of six magazines in one year. Discuss this fact from the viewpoint of the validity of the significance test and the interpretation of the results. Choose the best answer from the options below;

This is an SRS. This gives us no reason to believe our conclusions are suspect.

This is not an SRS. This gives us reason to believe our conclusions might be suspect.    

This is not an SRS. This gives us no reason to believe our conclusions are suspect.

This is an SRS. This gives us reason to believe our conclusions might be suspect.

Answer 1

Observed Frequencies
	Women	Men	General interest	Total
Not sexual	355	507	244	1106
Sexual	214	92	97	403
Total	569	599	341	1509

Expected frequency of a cell = sum of row*sum of column / total sum              

Expected Frequencies
	Women	Men	General interest	Total
Not sexual	417.0404	439.0285	249.9311	1106
Sexual	151.9596	159.9715	91.0689	403
Total	569	599	341	1509

	(fo-fe)^2/fe
Not sexual	9.2294	10.5235	0.1407
Sexual	25.3292	28.8809	0.3863

Null and Alternative hypothesis:  

Ho: factors are independent.  

H1: factor are dependent.  

Test statistic:  

χ² = ∑ ((fo-fe)²/fe) = 74.49

df = (r-1)(c-1) =   2

p-value = CHISQ.DIST.RT(74.49, 2) = 0.0000

Decision:  
p-value < α, Reject the null hypothesis.   

(B) Conclusion:

Reject the null hypothesis. There is significant evidence of an association between target audience and model dress.

(C) This is not an SRS. This gives us reason to believe our conclusions might be suspect.