Question

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	57	10	321	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 = p₂ = p₃ = p₄ = 57
H_a: H₀ is not true.H₀: p₁ = 69.738, p₂ = 12.608, p₃ = 289.196, p₄ = 22.458
H_a: H₀ is not true.    H₀: p₁ = 0.177, p₂ = 0.032, p₃ = 0.734, p₄ = 0.057
H_a: H₀ is not true.H₀: p₁ = p₂ = p₃ = p₄ = 0.177
H_a: H₀ is not true.H₀: p₁ = p₂ = p₃ = p₄ = 69.738
H_a: H₀ is not true.

Calculate the test statistic. (Round your answer to two decimal places.)
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 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.     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.Reject H₀. There is convincing evidence to conclude that the proportions of appearances in commercials are not the same as the census proportions.

Answer 1

The statistical software output for this problem is :

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

Test statistics = 18.42

P-value = 0.0004

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