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	354	504	244	1102
Sexual	216	88	103	407
Total	570	592	347	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) Conditional distribution of model dress for each audience:

	Women	Men	General interest
Not sexual	354 / 570 = 0.621	504 / 592 = 0.851	244 / 347 = 0.703
Sexual	216 / 570 = 0.379	88 / 592 = 0.149	103 / 347 = 0.297

b)

Observed Frequencies
	Women	Men	General interest	Total
Not sexual	354	504	244	1102
Sexual	216	88	103	407
Total	570	592	347	1509
Expected Frequencies
	Women	Men	General interest	Total
Not sexual	570 * 1102 / 1509 = 416.2624	592 * 1102 / 1509 = 432.3287	347 * 1102 / 1509 = 253.4089	1102
Sexual	570 * 407 / 1509 = 153.7376	592 * 407 / 1509 = 159.6713	347 * 407 / 1509 = 93.5911	407
Total	570	592	347	1509
	(fo-fe)²/fe
Not sexual	(354 - 416.2624)²/416.2624 = 9.3129	(504 - 432.3287)²/432.3287 = 11.8816	(244 - 253.4089)²/253.4089 = 0.3493
Sexual	(216 - 153.7376)²/153.7376 = 25.2158	(88 - 159.6713)²/159.6713 = 32.1709	(103 - 93.5911)²/93.5911 = 0.9459

Test statistic:

χ² = ∑ ((fo-fe)²/fe) = 79.88

df = (r-1)(c-1) = 2

p-value:

p-value = CHISQ.DIST.RT(79.8765, 2) = 0.0000

Decision:

p-value < α, Reject the null hypothesis.