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 | 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, 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} =
*p*_{2} = *p*_{3} =
*p*_{4} = 0.177

*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} = 70.8,
*p*_{2} = 12.8, *p*_{3} = 293.6,
*p*_{4} = 22.8

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

*H*_{0}: *p*_{1} =
*p*_{2} = *p*_{3} =
*p*_{4} = 70.8

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

*H*_{0}: *p*_{1} =
*p*_{2} = *p*_{3} =
*p*_{4} = 60

*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?

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.

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.

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 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,...

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,...

The authors of a paper studied a random sample of 355 Twitter
users. For each Twitter user in the sample, the "tweets" sent
during a particular time period were analyzed and the Twitter user
was classified into one of the following categories based on the
type of messages they usually sent.
Category
Description
IS
Information sharing
OC
Opinions and complaints
RT
Random
thoughts
ME
Me now
(what I am doing now)
O
Other
The accompanying table gives the observed counts...

The authors of a paper studied a random sample of 353 Twitter
users. For each Twitter user in the sample, the tweets sent during
a particular time period were analyzed and the Twitter user was
classified into one of the following categories based on the type
of messages they usually sent.
Category
Description
IS
Information sharing
OC
Opinions and complaints
RT
Random thoughts
ME
Me
now (what I am doing now)
O
Other
The accompanying table gives the observed counts...

Birds use color to select and avoid certain types of food. The
authors of a particular article studied the pecking behavior of
1-day-old bobwhites. In an area painted white, they inserted four
pins with different colored heads. The color of the pin chosen on
the bird's first peck was noted for each of 34 bobwhites, resulting
in the accompanying table.
Color
First
Peck
Frequency
Blue
15
Green
9
Yellow
7
Red
3
Do these data provide evidence of a color...

USA Today ("Hybrid Car Sales Rose 81% Last Year," April
25, 2005) reported the top five states for sales of hybrid cars in
2004 as California, Virginia, Washington, Florida, and Maryland.
Suppose that each car in a sample of 2004 hybrid car sales is
classified by state where the sale took place. Sales from states
other than the top five were excluded from the sample, resulting in
the accompanying table.
State
Observed
Frequency
California
255
Virginia
56
Washington
37
Florida...

USA Today ("Hybrid Car Sales Rose 81% Last Year," April
25, 2005) reported the top five states for sales of hybrid cars in
2004 as California, Virginia, Washington, Florida, and Maryland.
Suppose that each car in a sample of 2004 hybrid car sales is
classified by state where the sale took place. Sales from states
other than the top five were excluded from the sample, resulting in
the accompanying table.
State
Observed Frequency
California
255
Virginia
56
Washington
37
Florida...

The authors of a paper classified characters who were depicted
smoking in movies released between a certain range of years. The
smoking characters were classified according to sex and whether the
character type was positive, negative, or neutral. The resulting
data is given in the accompanying table.
Assume that it is reasonable to consider this sample of smoking
movie characters as representative of smoking movie characters. Do
the data provide evidence of an association between sex and
character type for...

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