Question

# The authors of a paper concerned about racial stereotypes in television counted the number of times...

The authors of a paper concerned about racial stereotypes in television counted the number of times that characters of different ethnicities appeared in commercials aired on a certain city's television stations, resulting in the data in the accompanying table.

Ethnicity African-
American
Asian Caucasian Hispanic
Observed Frequency 59 11 332 6

Based on the 2000 Census, the proportion of the U.S. population falling into each of these four ethnic groups are 0.177 for African-American, 0.032 for Asian, 0.734 for Caucasian, and 0.057 for Hispanic. Do the data provide sufficient evidence to conclude that the proportions appearing in commercials are not the same as the census proportions? Test the relevant hypotheses using a significance level of 0.01.

Let p1, p2, p3, and p4 be the proportions of appearances of the four ethnicities across all commercials.

State the null and alternative hypotheses.

H0: p1 = 72.216, p2 = 13.056, p3 = 299.472, p4 = 23.256
Ha: H0 is not true.H0: p1 = p2 = p3 = p4 = 72.216
Ha: H0 is not true.    H0: p1 = p2 = p3 = p4 = 59
Ha: H0 is not true.H0: p1 = 0.177, p2 = 0.032, p3 = 0.734, p4 = 0.057
Ha: H0 is not true.H0: p1 = p2 = p3 = p4 = 0.177
Ha: H0 is not true.

χ2 =

What is the P-value for the test? (Round your answer to four decimal places.)
P-value =

What can you conclude?

Reject H0. There is convincing evidence to conclude that the proportions of appearances in commercials are not the same as the census proportions.Reject H0. There is not enough evidence to conclude that the proportions of appearances in commercials are not the same as the census proportions.     Do not reject H0. There is not enough evidence to conclude that the proportions of appearances in commercials are not the same as the census proportions.Do not reject H0. There is convincing evidence to conclude that the proportions of appearances in commercials are not the same as the census proportions.

The statistical software output for this problem is :

H0: p1 = 0.177, p2 = 0.032, p3 = 0.734, p4 = 0.057
Ha: H0 is not true.

Test statistics = 19.08

P-value = 0.0003

Reject H0. There is convincing evidence to conclude that the proportions of appearances in commercials are not the same as the census proportions.

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