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

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 =

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**

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
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,...

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