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	346	525	260	1131
Sexual	212	93	73	378
Total	558	618	333	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 =

Answer 1

(a)

Following table shows the conditional distribution :

	Magazine readership
Model dress	Women	Men	General interest
Not sexual	((346*100)/558)=62.01%	((525*100)/618)=84.95%	((260*100)/333)=78.08%
Sexual	((212*100)/558)=37.99%	((93*100)/618)=15.05%	((73*100)/333)=21.92%
Total	100%	100%	100%

Following is the graph:

(b)

Following table shows the outcome of chi square independence test generated by excel:

Chi-square Contingency Table Test for Independence
			Women	Men	General interest	Total
	Not sexual	Observed	346	525	260	1131
		Expected	418.22	463.19	249.58	1131.00
		O - E	-72.22	61.81	10.42	0.00
		(O - E)² / E	12.47	8.25	0.43	21.15
		% of row	30.6%	46.4%	23.0%	100.0%
		% of column	62.0%	85.0%	78.1%	75.0%
		% of total	22.9%	34.8%	17.2%	75.0%
	Sexual	Observed	212	93	73	378
		Expected	139.78	154.81	83.42	378.00
		O - E	72.22	-61.81	-10.42	0.00
		(O - E)² / E	37.32	24.68	1.30	63.29
		% of row	56.1%	24.6%	19.3%	100.0%
		% of column	38.0%	15.0%	21.9%	25.0%
		% of total	14.0%	6.2%	4.8%	25.0%
	Total	Observed	558	618	333	1509
		Expected	558.00	618.00	333.00	1509.00
		O - E	0.00	0.00	0.00	0.00
		(O - E)² / E	49.79	32.92	1.74	84.45
		% of row	37.0%	41.0%	22.1%	100.0%
		% of column	100.0%	100.0%	100.0%	100.0%
		% of total	37.0%	41.0%	22.1%	100.0%
			84.45	chi-square
			2	df
			4.59E-19	p-value

Since p-value is very small (less than 0.01)so there is very strong evidence that target audience affects model dress.

Conclusion:

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