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.
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
What is the P-value for the test? (Round your answer to four decimal places.)
|observed frequency,O||proportion||Expected frequency , E= N*P||(O-E)^2|
|N = 398||=17.568|
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
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