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 | 59 | 11 | 332 | 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 *p*_{1}, *p*_{2},
*p*_{3}, and *p*_{4} be the
proportions of appearances of the four ethnicities across all
commercials.

State the null and alternative hypotheses.

*H*_{0}: *p*_{1} = 72.216,
*p*_{2} = 13.056, *p*_{3} = 299.472,
*p*_{4} = 23.256

*H*_{a}: *H*_{0} is not
true.*H*_{0}: *p*_{1} =
*p*_{2} = *p*_{3} =
*p*_{4} = 72.216

*H*_{a}: *H*_{0} is not
true. *H*_{0}:
*p*_{1} = *p*_{2} =
*p*_{3} = *p*_{4} = 59

*H*_{a}: *H*_{0} is not
true.*H*_{0}: *p*_{1} = 0.177,
*p*_{2} = 0.032, *p*_{3} = 0.734,
*p*_{4} = 0.057

*H*_{a}: *H*_{0} is not
true.*H*_{0}: *p*_{1} =
*p*_{2} = *p*_{3} =
*p*_{4} = 0.177

*H*_{a}: *H*_{0} is not
true.

Calculate the test statistic. (Round your answer to two decimal
places.)

*χ*^{2} =

What is the *P*-value for the test? (Round your answer to
four decimal places.)

*P*-value =

What can you conclude?

Reject *H*_{0}. There is convincing evidence to
conclude that the proportions of appearances in commercials are not
the same as the census proportions.Reject *H*_{0}.
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
*H*_{0}. 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 *H*_{0}.
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 :

*H*_{0}: *p*_{1} = 0.177,
*p*_{2} = 0.032, *p*_{3} = 0.734,
*p*_{4} = 0.057

*H*_{a}: *H*_{0} is not
true.

Test statistics = 19.08

P-value = 0.0003

Reject *H*_{0}. There is convincing evidence to
conclude that the proportions of appearances in commercials are not
the same as the census proportions.

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
60
10
324
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,...

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,...

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The authors of a paper studied a random sample of 353 Twitter
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Category
Description
IS
Information sharing
OC
Opinions and complaints
RT
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ME
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