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	344	530	250	1124
Sexual	208	96	81	385
Total	552	626	331	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) the conditional porobability distribution of the model is given as

Model dress	Women	Men	General interest	Total
Not sexual	0.2280	0.3512	0.1657	0.7449
Sexual	0.1378	0.0636	0.0537	0.2551
Total	0.3658	0.4148	0.2194	1.0000

the bar diagram is given as

(2) here we use chi-square test with

null hypothesis H0: there is no association between magazine readership and model dress

alternate hypothesis Ha: there is association between magazine readership and model dress

the chi-square=sum((O-E)2/E)=77.32 with (r-1)(c-1)=(3-1)*(2-1)=2 df with p-value=0.0000

the critical chi-square(0.05,2)=5.99 is less than calculated chi-square =77.32, so we reject null hypothesis and conclude that there is association between magzine readership and model dress

	Observed(O)	Expected(E)	E	(O-E)	(O-E)2/E
	344	1124*552/1509	411.17	-67.17	10.9716
	530	1124*626/1509	466.28	63.72	8.706279
	250	1124*331/1509	246.55	3.45	0.048275
	208	385*552/1509	140.83	67.17	32.03138
	96	385*626/1509	159.72	-63.72	25.41781
	81	385*331/1509	84.45	-3.45	0.140939
sum=	1509	0	1509	1.42E-14	77.32
critical chi-square	5.99	p-value=	0.0000