Question

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 for the five categories (approximate values read from a graph in the paper).

Twitter Type | IS | OC | RT | ME | O |
---|---|---|---|---|---|

Observed count | 53 | 63 | 64 | 99 | 74 |

Carry out a hypothesis test to determine if there is convincing evidence that the proportions of Twitter users falling into each of the five categories are not all the same. Use a significance level of 0.05. (Hint: See Example 12.2.)

Let *p*_{1}, *p*_{2},
*p*_{3}, *p*_{4}, and
*p*_{5} be the proportions of Twitter users falling
into the five categories.

State the appropriate null and alternative hypotheses.

*H*_{0}: *p*_{1} =
*p*_{2} = *p*_{3} =
*p*_{4} = *p*_{5} = 353

*H*_{a}: *H*_{0} is not
true.*H*_{0}: *p*_{1} =
*p*_{2} = *p*_{3} =
*p*_{4} = *p*_{5} = 70

*H*_{a}: *H*_{0} is not
true. *H*_{0}:
*p*_{1} = *p*_{2} =
*p*_{3} = *p*_{4} =
*p*_{5} = 0.05

*H*_{a}: *H*_{0} is not
true.*H*_{0}: *p*_{1} =
*p*_{2} = *p*_{3} =
*p*_{4} = *p*_{5} = 0.2

*H*_{a}: *H*_{0} is not
true.*H*_{0}: *p*_{1} =
*p*_{2} = *p*_{3} =
*p*_{4} = *p*_{5} = 0.5

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

Find the test statistic and *P*-value. (Use technology.
Round your test statistic to three decimal places and your
*P*-value to four decimal places.)

*X*^{2}=

*P*-value=

State the conclusion in the problem context.

Do not reject *H*_{0}. There is convincing
evidence to conclude that the proportions of Twitter users falling
into the five categories are not all the same.Reject
*H*_{0}.

There is convincing evidence to conclude that the proportions of Twitter users falling into the five categories are not all the same.

Reject *H*_{0}. There is not convincing evidence
to conclude that the proportions of Twitter users falling into the
five categories are not all the same.Do not reject
*H*_{0}.

There is not convincing evidence to conclude that the proportions of Twitter users falling into the five categories are not all the same.

Answer #1

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 350 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 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
57
10
321
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
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,...

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
250
Virginia
54
Washington
31
Florida...

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
8 Yellow 7 Red 4 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...

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