In what ways do advertisers in magazines use sexual imagery to appeal to youth?
ID: 3182743 • Letter: I
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.
(a) Summarize the data numerically and graphically. (Compute the conditional distribution of model dress for each audience. Round your answers to three decimal places.)
(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 = 0.01. Round your value for 2 to two decimal places, and round your P-value to four decimal places.)
Conclusion
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.
Reject the null hypothesis. There is 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.
(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.
This is an SRS. This gives us reason to believe our conclusions might be suspect.
This is an SRS. This gives us no reason to believe our conclusions are suspect.
This is not 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.
Magazine readership Model dress Women Men General interest Total Not sexual 347 504 247 1098 Sexual 202 93 116 411 Total 549 597 363 1509Explanation / Answer
Part a
The conditional distribution of the magazine readership and model dress for each audience is given as below:
Women
Men
General
Total
Not Sexual
347/1509 = 0.230
504/1509 = 0.334
247/1509 = 0.164
0.728
Sexual
202/1509 = 0.134
93/1509 = 0.062
116/1509 = 0.077
0.272
Total
0.364
0.396
0.241
1.000
The bar graph for comparison is given as below:
Part b
Here, we have to perform the chi square test for independence.
Null hypothesis: H0: The variable magazine readership and type of model dress are independent from each other.
Alternative hypothesis: Ha: The variable magazine readership and type of model dress are not independent from each other.
We are given level of significance = alpha = 0.01
The test statistic formula is given as below:
Chi square = [(O – E)^2/E]
The calculations tables are given as below:
Observed Frequencies
Magazine Readership
Model dress
Women
Men
General
Total
Not sexual
347
504
247
1098
Sexual
202
93
116
411
Total
549
597
363
1509
Expected frequencies = Row total * Column total / Grand Total
Expected Frequencies
Magazine Readership
Model dress
Women
Men
General
Total
Not sexual
399.4712
434.3976
264.1312
1098
Sexual
149.5288
162.6024
98.86879
411
Total
549
597
363
1509
Calculations
fo-fe
-52.4712
69.60239
-17.1312
52.47117
-69.6024
17.13121
(fo-fe)^2/fe
6.892172
11.15221
1.111109
18.41266
29.79349
2.968363
Data
Level of Significance
0.05
Number of Rows
2
Number of Columns
3
Degrees of Freedom
2
Results
Critical Value
5.991
Chi-Square Test Statistic
70.33
p-Value
0.000
Reject the null hypothesis
We reject the null hypothesis that the variable magazine readership and type of model dress are independent from each other.
We conclude that the variable magazine readership and type of model dress are not independent from each other.
Reject the null hypothesis. There is significant evidence of an association between target audience and model dress.
Part C
Interpretation:
This is not an SRS. This gives us reason to believe our conclusions might be suspect.
Women
Men
General
Total
Not Sexual
347/1509 = 0.230
504/1509 = 0.334
247/1509 = 0.164
0.728
Sexual
202/1509 = 0.134
93/1509 = 0.062
116/1509 = 0.077
0.272
Total
0.364
0.396
0.241
1.000
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