Question

Random samples of people ages 15−24 and of people ages 25−34 were asked about their preferred method of (remote) communication with friends. The respondents were asked to select one of the methods from the following list: cell phone, instant message, e-mail, other.

Preferred
Communication Method |
|||||

Age |
Cell
Phone |
Instant
Message |
Email |
Other |
Row
Total |

15-24 | 42 | 45 | 7 | 6 | 100 |

25-34 | 45 | 26 | 15 | 14 | 100 |

Column
Total |
87 | 71 | 22 | 20 | 200 |

(i) Make a cluster bar graph showing the percentages in each age group who selected each method. (In the graphs, cyan represents ages 15-24, and gray represents ages 25-34.)

(ii) Test whether the two populations share the same proportions of preferences for each type of communication method. Use α = 0.05.

(a) What is the level of significance?

**0.05**

(b) Find the value of the chi-square statistic for the sample.
(Round the expected frequencies to at least three decimal places.
Round the test statistic to three decimal places.)

Are all the expected frequencies greater than 5?

**Yes**

What sampling distribution will you use?

**chi-square**

What are the degrees of freedom?

(c) Find or estimate the *P*-value of the sample test
statistic. (Round your answer to three decimal places.)

*p*-value > 0.100

0.050 < *p*-value <
0.100

0.025 < *p*-value < 0.050

0.010 < *p*-value < 0.025

0.005 < *p*-value < 0.010

*p*-value < 0.005

Answer #1

The statistical software output for this problem is :

Level of significance = 0.05

chi-square statistic = 11.297

degrees of freedom = 3

0.010 < *p*-value < 0.025

The age distribution of the Canadian population and the age
distribution of a random sample of 455 residents in the Indian
community of a village are shown below.
Age (years)
Percent of Canadian Population
Observed Number
in the Village
Under 5
7.2%
49
5 to 14
13.6%
76
15 to 64
67.1%
283
65 and older
12.1%
47
Use a 5% level of significance to test the claim that the age
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The dice were taken off the table and tested one at a time. One die
was rolled 300 times and the following frequencies were
recorded.
Outcome 1 2 3
4 5 6
Observed frequency O 60 44
59 34 46 57
Do these data indicate that the die is unbalanced? Use a 1% level
of significance. Hint: If the die is balanced, all outcomes should
have the same expected...

The following table shows ceremonial ranking and type of pottery
sherd for a random sample of 434 sherds at an archaeological
location.
Ceremonial Ranking Cooking Jar Sherds Decorated Jar Sherds
(Noncooking) Row Total
A 89 46 135
B 93 52 145
C 79 75 154
Column Total 261 173 434
Use a chi-square test to determine if ceremonial ranking and
pottery type are independent at the 0.05 level of significance.
(a) What is the level of significance?
State the null...

The director of library services at a college did a survey of
types of books (by subject) in the circulation library. Then she
used library records to take a random sample of 888 books checked
out last term and classified the books in the sample by subject.
The results are shown below.
Subject Area Percent of Books on Subject in Circulation Library
on This Subject Number of Books in Sample on This Subject Business
32% 263 Humanities 25% 225 Natural...

The age distribution of the Canadian population and the age
distribution of a random sample of 455 residents in the Indian
community of a village are shown below.
Age (years)
Percent of Canadian Population
Observed Number
in the Village
Under 5
7.2%
50
5 to 14
13.6%
69
15 to 64
67.1%
289
65 and older
12.1%
47
Use a 5% level of significance to test the claim that the age
distribution of the general Canadian population fits the age...

The following table shows the Myers-Briggs personality
preferences for a random sample of 406 people in the listed
professions. E refers to extroverted and I refers to
introverted.
Personality Type
Occupation
E
I
Row
Total
Clergy (all denominations)
62
45
107
M.D.
70
92
162
Lawyer
61
76
137
Column
Total
193
213
406
Use the chi-square test to determine if the listed occupations
and personality preferences are independent at the 0.05 level of
significance.
(a) What is the level...

The following table shows the Myers-Briggs personality
preferences for a random sample of 406 people in the listed
professions. E refers to extroverted and I refers to
introverted.
Personality Type
Occupation
E
I
Row
Total
Clergy (all denominations)
61
46
107
M.D.
64
98
162
Lawyer
56
81
137
Column
Total
181
225
406
Use the chi-square test to determine if the listed occupations
and personality preferences are independent at the 0.05 level of
significance.
(a) What is the level...

The following table shows the Myers-Briggs personality
preferences for a random sample of 406 people in the listed
professions. E refers to extroverted and I refers to
introverted.
Personality Type
Occupation
E
I
Row
Total
Clergy (all denominations)
64
43
107
M.D.
64
98
162
Lawyer
61
76
137
Column
Total
189
217
406
Use the chi-square test to determine if the listed occupations
and personality preferences are independent at the 0.05 level of
significance.
(a) What is the level...

The following table shows ceremonial ranking and type of pottery
sherd for a random sample of 434 sherds at an archaeological
location.
Ceremonial Ranking
Cooking Jar
Sherds
Decorated Jar Sherds
(Noncooking)
Row
Total
A
85
50
135
B
96
49
145
C
81
73
154
Column
Total
262
172
434
Use a chi-square test to determine if ceremonial ranking and
pottery type are independent at the 0.05 level of significance.
(a) Find the value of the chi-square statistic for the...

The following table shows the Myers-Briggs personality
preferences for a random sample of 406 people in the listed
professions. E refers to extroverted and I refers to
introverted.
Personality Type
Occupation
E
I
Row
Total
Clergy (all denominations)
61
46
107
M.D.
71
91
162
Lawyer
54
83
137
Column Total
186
220
406
Use the chi-square test to determine if the listed occupations
and personality preferences are independent at the 0.05 level of
significance.
(a) What is the level...

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