In what ways do advertisers in magazines use sexual imagery to appeal to youth?

Question

In what ways do advertisers in magazines use sexual imagery to appeal to youth? One study classified each of 1500 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 age group of the intended readership. Here is a summary of the data.

Perform the significance test that compares the model dress for the age groups of magazine readership. Summarize the results of your test. (Use = 0.05. Round your 2 to three decimal places and round your P-value to four decimal places.)

Give your conclusion.

Fail to reject the null hypothesis. There is not significant evidence of an association between model dress and age group.Reject the null hypothesis. There is not significant evidence of an association between model dress and age group.    Fail to reject the null hypothesis. There is significant evidence of an association between model dress and age group.Reject the null hypothesis. There is significant evidence of an association between model dress and age group.

Magazine readership age group Model dress Young adult Mature adult Not sexual (percent) 72.8% 75.6% Sexual (percent) 27.2% 24.4% Number of ads 1000 500

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

H0: Model dress and age group are independent.
Ha: Model dress and age group are not independent.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square test for independence.

Analyze sample data. Applying the chi-square test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

DF = (r - 1) * (c - 1) = (2 - 1) * (2 - 1)
D.F = 1
Er,c = (nr * nc) / n

2 = [ (Or,c - Er,c)2 / Er,c ]
2 =

where DF is the degrees of freedom.

The P-value is the probability that a chi-square statistic having 1 degrees of freedom is more extreme than 1.349.

We use the Chi-Square Distribution Calculator to find P(2 > 1.349) = 0.245

Interpret results. Since the P-value (0.245) is greater than the significance level (0.05), we have to accept the null hypothesis. Thus, we conclude that there is not a relationship between model dress and age group.

Fail to reject the null hypothesis. There is not significant evidence of an association between model dress and age group.

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