Question

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 of significance?

State the null and alternate hypotheses.

*H*_{0}: Myers-Briggs preference and profession
are not independent

*H*_{1}: Myers-Briggs preference and profession are
independent.

*H*_{0}: Myers-Briggs preference and profession
are independent

*H*_{1}: Myers-Briggs preference and profession are
independent.

*H*_{0}: Myers-Briggs preference and profession
are independent

*H*_{1}: Myers-Briggs preference and profession are
not independent.

*H*_{0}: Myers-Briggs preference and profession
are not independent

*H*_{1}: Myers-Briggs preference and profession 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?

uniform

chi-square

normal

Student's *t*

binomial

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 insufficient evidence to conclude that Myers-Briggs preference and the profession are not independent.

At the 5% level of significance, there is sufficient evidence to conclude that Myers-Briggs preference and the profession are not independent.

Answer #1

The statistical software output for this problem is:

Hence,

a) Level of significance = 0.05

Hypotheses: *H*_{0}: Myers-Briggs preference and
profession are independent

*H*_{1}: Myers-Briggs preference and profession are
not independent.

**Option C** is correct.

b) Test statistic = 6.361

Yes

chi - square

Degrees of freedom = 2

c) 0.025 < *p*-value < 0.050

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

e) At the 5% level of significance, there is sufficient evidence to conclude that Myers-Briggs preference and the profession are not independent.

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...

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)
58
49
107
M.D.
63
99
162
Lawyer
51
86
137
Column
Total
172
234
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)
63
44
107
M.D.
71
91
162
Lawyer
54
83
137
Column Total
188
218
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 519 people in the listed
professions. T refers to thinking and F refers to feeling.
Personality Type
Occupation
T
F
Row
Total
Clergy (all denominations)
55
93
148
M.D.
79
80
159
Lawyer
120
92
212
Column Total
254
265
519
Use the chi-square test to determine if the listed occupations
and personality preferences are independent at the 0.01 level of
significance.
(a) What is the level...

Question 21
Question text
The following table shows the Myers-Briggs personality
preferences for a random sample of 406 people in the listed
professions.
Occupation
Extroverted
Introverted
Row Total
Clergy (all denominations)
62
42
104
M.D.
70
95
165
Lawyer
56
81
137
Column Total
188
218
406
Use the chi-square test to determine if the listed occupations
and personality preferences are independent at the 0.05 level of
significance. Given P-Value < 0.005, will you reject or fail to
reject...

The following table shows the Myers-Briggs personality
preferences for a random sample of 519 people in the listed
professions. T refers to thinking and F refers to feeling.
Personality Type
Occupation
T
F
Row
Total
Clergy (all denominations)
53
95
148
M.D.
72
87
159
Lawyer
120
92
212
Column
Total
245
274
519
Use the chi-square test to determine if the listed occupations
and personality preferences are independent at the 0.01 level of
significance.
(a) What is the level...

The following table shows the Myers-Briggs personality
preference and area of study for a random sample of 519 college
students. In the table, IN refers to introvert, intuitive; EN
refers to extrovert, intuitive; IS refers to introvert, sensing;
and ES refers to extrovert, sensing.
Myers-Briggs
Preference
Arts &
Science
Business
Allied
Health
Row
Total
IN
63
9
24
96
EN
85
44
25
154
IS
52
36
27
115
ES
79
47
28
154
Column
Total
279
136
104
519...

The following table shows the Myers-Briggs personality
preference and area of study for a random sample of 519 college
students. In the table, IN refers to introvert, intuitive; EN
refers to extrovert, intuitive; IS refers to introvert, sensing;
and ES refers to extrovert, sensing.
Myers-Briggs
Preference
Arts &
Science
Business
Allied
Health
Row
Total
IN
61
9
26
96
EN
85
38
31
154
IS
58
38
19
115
ES
72
39
43
154
Column
Total
276
124
119
519...

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