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	342	529	249	1120
Sexual	210	86	93	389
Total	552	615	342	1509

(A) Summarize the data numerically and graphically. (Compute the conditional distribution of model dress for each audience. Round your answers to three decimal places.)

	Women	Men	General
Not sexual
Sexual

(B) 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 =

Conclusion

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

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

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

(d)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.

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

(b)This gives us no reason to believe our conclusions are suspect.     

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

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

Answer 1

(A)

Following table shows the conditional distribution of model dress:

	Women	Men	General
Not sexual	342/552=0.620	529/615=0.860	249/342=0.728
Sexual	210/552=0.380	86/615=0.140	93/342=0.272

Following is the graph:

(B)

Expected frequencies will be calculated as follows:

Following table shows the expected frequencies:

	Women	Men	General	Total
Not sexual	409.702	456.461	253.837	1120
Sexual	142.298	158.539	88.163	389
Total	552	615	342	1509

Following table shows the calculations for chi square test statistics:

O	E	(O-E)^2/E
342	409.702	11.18754803
210	142.298	32.21099948
529	456.461	11.52761467
86	158.539	33.18998178
249	253.837	0.092171626
93	88.163	0.265378549
Total		88.47369414

The test statistics is:

Degree of freedom: df =( number of rows -1)*(number of columns-1) = (3-1)*(2-1)=2

The p-value is:

p-value = 0.0000

Since p-value is less than 0.01 so we reject the null hypothesis.

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

(C)

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