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 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 =

 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