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	58	12	322	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.

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 =

Answer 1

observed frequency,O	proportion	Expected frequency , E= N*P	(O-E)^2
58	0.177	70.446	154.9029	2.1989
12	0.032	12.736	0.5417	0.0425
322	0.734	292.132	892.0974	3.0537
6	0.057	22.686	278.4226	12.2729
N = 398				=17.568

Test statistc

= 17.57

P- VALUE

degree of freedom ,

df = (r-1)(c-1)= 3*1 =3

P- value with test statistic = 17.57 and degree of freedom, df = 3 is

p-value = 0.000539

= 0.0005