Question

Mr. Acosta, a sociologist, is doing a study to see if there is a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred. A random sample of 93 adults revealed the following data. Test whether age and type of movie preferred are independent at the 0.05 level.

Person's
Age |
||||

Movie |
18-23
yr |
24-29
yr |
30-35
yr |
Row
Total |

Drama | 9 | 12 | 13 | 34 |

Science Fiction | 14 | 11 | 5 | 30 |

Comedy | 9 | 8 | 12 | 29 |

Column
Total |
32 | 31 | 30 | 93 |

(a) What is the level of significance?

State the null and alternate hypotheses.

*H*_{0}: Age and movie preference are not
independent.

*H*_{1}: Age and movie preference are
independent.

*H*_{0}: Age and movie preference are
independent.

*H*_{1}: Age and movie preference are
independent.

*H*_{0}: Age and movie preference are
independent.

*H*_{1}: Age and movie preference are not
independent.

*H*_{0}: Age and movie preference are not
independent.

*H*_{1}: Age and movie preference are not
independent.

(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

No

What sampling distribution will you use?

binomial

uniform Student's *t*

chi-square

normal

What are the degrees of freedom?

(c) Find or estimate the *P*-value of the sample test
statistic.

*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

(d) Based on your answers in parts (a) to (c), will you reject or
fail to reject the null hypothesis of independence?

Since the *P*-value > *α*, we fail to reject
the null hypothesis.

Since the *P*-value > *α*, we reject the null
hypothesis.

Since the *P*-value ≤ *α*, we reject the null
hypothesis.

Since the *P*-value ≤ *α*, we fail to reject the
null hypothesis.

(e) Interpret your conclusion in the context of the
application.

At the 5% level of significance, there is sufficient evidence to conclude that age of young adult and movie preference are not independent.

At the 5% level of significance, there is insufficient evidence to conclude that age of young adult and movie preference are not independent.

Answer #1

The statistical software output for this problem is:

Hence,

a) Level of significance = 0.05

Hypotheses: *H*_{0}: Age and movie preference are
independent.

*H*_{1}: Age and movie preference are not
independent.

**Option C** is correct.

b) Test statistic = 5.841

Yes

Chi - square

Degrees of freedom = 4

c) *P*-value > 0.100

d) Since the *P*-value > *α*, we fail to reject
the null hypothesis.

e) At the 5% level of significance, there is insufficient evidence to conclude that age of young adult and movie preference are not independent.

Mr. Acosta, a sociologist, is doing a study to see if there is a
relationship between the age of a young adult (18 to 35 years old)
and the type of movie preferred. A random sample of 93 adults
revealed the following data. Test whether age and type of movie
preferred are independent at the 0.05 level.
Person's
Age
Movie
18-23
yr
24-29
yr
30-35
yr
Row
Total
Drama
7
12
15
34
Science Fiction
14
9
7
30
Comedy...

Mr. Acosta, a sociologist, is doing a study to see if there is a
relationship between the age of a young adult (18 to 35 years old)
and the type of movie preferred. A random sample of 93 adults
revealed the following data. Test whether age and type of movie
preferred are independent at the 0.05 level.
Person's
Age
Movie
18-23
yr
24-29
yr
30-35
yr
Row
Total
Drama
9
15
10
34
Science Fiction
9
10
11
30
Comedy...

Mr. Acosta, a sociologist, is doing a study to see if there is a
relationship between the age of a young adult (18 to 35 years old)
and the type of movie preferred. A random sample of 93 adults
revealed the following data. Test whether age and type of movie
preferred are independent at the 0.05 level.
Person's
Age
Movie
18-23
yr
24-29
yr
30-35
yr
Row
Total
Drama
6
14
14
34
Science Fiction
12
9
9
30
Comedy...

Mr. Acosta, a sociologist, is doing a study to see if there is a
relationship between the age of a young adult (18 to 35 years old)
and the type of movie preferred. A random sample of 93 adults
revealed the following data. Test whether age and type of movie
preferred are independent at the 0.05 level.
Person's
Age
Movie
18-23
yr
24-29
yr
30-35
yr
Row
Total
Drama
8
12
14
34
Science Fiction
14
8
8
30
Comedy...

Mr. Acosta, a sociologist, is doing a study to see if there is a
relationship between the age of a young adult (18 to 35 years old)
and the type of movie preferred. A random sample of 93 adults
revealed the following data. Test whether age and type of movie
preferred are independent at the 0.05 level.
Person's
Age
Movie
18-23
yr
24-29
yr
30-35
yr
Row
Total
Drama
7
16
11
34
Science Fiction
11
12
7
30
Comedy...

Mr. Acosta, a sociologist, is doing a study to see if there is a
relationship between the age of a young adult (18 to 35 years old)
and the type of movie preferred. A random sample of 93 adults
revealed the following data. Test if age and type are movie
preferred are independent at the 0.05 level. Person’s AgeMovie
18-23 yr 24-29 yr 30-35 yr Total Musical 8 15 11 34 Science Fiction
12 10 8 30 Comedy 9 8...

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)
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 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)
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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