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	510	245	1099
Sexual	219	89	102	410
Total	563	599	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 =

Conclusion

Fail to reject the null hypothesis. There is 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 not significant evidence of an association between target audience and model dress.Reject the null hypothesis. There is not 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 not an SRS. This gives us no reason to believe our conclusions are suspect.This is an SRS. This gives us reason to believe our conclusions might be suspect.    This is not 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.

Answer 1

Solution:-

a)

b)

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

H₀: Target audience and model dress are independent.
H_a: Target audience and model dress 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) * (3 - 1)
D.F = 2
E_r,c = (n_r * n_c) / n

Χ² = 85.89

where DF is the degrees of freedom.

The P-value is the probability that a chi-square statistic having 2 degrees of freedom is more extreme than 85.89.

We use the Chi-Square Distribution Calculator to find P(Χ² > 85.89) = less than 0.0001

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we cannot accept the null hypothesis. Thus, we conclude that there is a relationship between Target audience and model dress.

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

c)

This is not an SRS. This gives us reason to believe our conclusions might be suspect.