The authors of a paper concerned about racial stereotypes intelevision counted the number of times that characters of differentethnicities appeared in commercials aired on a certain city'stelevision stations, resulting in the data in the accompanyingtable.

Ethnicity	African- American	Asian	Caucasian	Hispanic
Observed Frequency	56	12	320	6

Based on the 2000 Census, the proportion of the U.S. populationfalling into each of these four ethnic groups are 0.177 forAfrican-American, 0.032 for Asian, 0.734 for Caucasian, and 0.057for Hispanic. Do the data provide sufficient evidence to concludethat the proportions appearing in commercials are not the same asthe census proportions? Test the relevant hypotheses using asignificance level of 0.01.

Let p₁, p₂,p₃, and p₄ be theproportions of appearances of the four ethnicities across allcommercials.

State the null and alternative hypotheses.

H₀: p₁ =p₂ = p₃ =p₄ = 0.177
H_a: H₀ is nottrue.

H₀: p₁ =p₂ = p₃ =p₄ = 69.738
H_a: H₀ is nottrue.    

H₀: p₁ = 0.177,p₂ = 0.032, p₃ = 0.734,p₄ = 0.057
H_a: H₀ is nottrue.

H₀: p₁ =p₂ = p₃ =p₄ = 56
H_a: H₀ is nottrue.

H₀: p₁ = 69.738,p₂ = 12.608, p₃ = 289.196,p₄ = 22.458
H_a: H₀ is nottrue.

Calculate the test statistic. (Round your answer to two decimalplaces.)
?² =  

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

What can you conclude?

Do not reject H₀. There is convincingevidence to conclude that the proportions of appearances incommercials are not the same as the census proportions.

Reject H₀. There is not enough evidence toconclude that the proportions of appearances in commercials are notthe same as the censusproportions.     

Reject H₀. There is convincing evidence toconclude that the proportions of appearances in commercials are notthe same as the census proportions.

Do not reject H₀. There is not enoughevidence to conclude that the proportions of appearances incommercials are not the same as the census proportions.