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 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

Fail to 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 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 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 reason to believe our conclusions might be suspect.This is not an SRS. This gives us no reason to believe our conclusions are suspect.

Magazine readership Model dress Women Men General interest Total Not sexual 351 529 252 1132 Sexual 218 93 66 377 Total 569 622 318 1509

Explanation / Answer

Given table data is as below

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calculation formula for E table matrix

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expected frequecies calculated by applying E - table matrix formulae

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calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above

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set up null vs alternative as
null, Ho: no relation b/w X and Y OR X and Y are independent
alternative, H1: exists a relation b/w X and Y OR X and Y are dependent
level of significance, = 0.01
from standard normal table, chi square value at right tailed, ^2 /2 =9.21
since our test is right tailed,reject Ho when ^2 o > 9.21
we use test statistic ^2 o = (Oi-Ei)^2/Ei
from the table , ^2 o = 90.373
critical value
the value of |^2 | at los 0.01 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 3 - 1 ) = 1 * 2 = 2 is 9.21
we got | ^2| =90.373 & | ^2 | =9.21
make decision
hence value of | ^2 o | > | ^2 | and here we reject Ho
^2 p_value =0
ANSWERS
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null, Ho: no relation b/w X and Y OR X and Y are independent
alternative, H1: exists a relation b/w X and Y OR X and Y are dependent
test statistic: 90.373
critical value: 9.21
p-value:0
decision: reject the null hypothesis. There is significant evidence of an association between target audience and model dress                            

col1 col2 col3 row 1 351 529 252 1132 row 2 218 93 66 377 TOTALS 569 622 318 N = 1509

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