The article Racial Stereotypes in Children Television Commercials reported the f

Question

The article Racial Stereotypes in Children Television Commercials reported the following frequencies with which ethnic characters appeared in recoreded commercials that aired on Philadelphia television stations.

Ethinicity: Afri-Amer Asian Caucasion Hispanic

Frequency: 57 11 330 6

The 2000 census proportions for these four ethnic groups are .177, .032, .734, and .057, respectively. Does the data suggest that the proportions in commercials are different from the census proportions? Carry out a test of appropriate hypotheses using a significance level of 0.01. Use the rejection region method, not the p value method.

Explanation / Answer

This is a clear case of chi square distribution

the chi square statistic is calculated as = Summation ( observed -expected/expected)

= (57- 0.177*404)^2/0.177*404 + (11- 0.032*404)^2/0.032*404 + (330 -0.734*404)^2/0.734*404 + (6 -0.057*404)^2/0.057*404

= 19.5987

degrees of freedom = 4-1 =3

sincechi sqaure test statisitcs is greater than critical value we reject the null hypothesis

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