Question

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-BriggsPreference |
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 |

Use a chi-square test to determine if Myers-Briggs preference type is independent of area of study at the 0.05 level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses.

*H*_{0}: Myers-Briggs type and area of study are
not independent.

*H*_{1}: Myers-Briggs type and area of study are not
independent.

*H*_{0}: Myers-Briggs type and area of study are
independent.

*H*_{1}: Myers-Briggs type and area of study are
independent.

*H*_{0}: Myers-Briggs type and area of study are
independent.

*H*_{1}: Myers-Briggs type and area of study are not
independent.

*H*_{0}: Myers-Briggs type and area of study are
not independent.

*H*_{1}: Myers-Briggs type and area of study are
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?

YesNo

What sampling distribution will you use?

Student's *t*

uniform chi-square

normal

binomial

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

(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 Myers-Briggs type and area of study are not independent.

At the 5% level of significance, there is insufficient evidence to conclude that Myers-Briggs type and area of study 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 type and area
of study are independent.

*H*_{1}: Myers-Briggs type and area of study are not
independent.

**Option C** is correct.

b) Test statistic = **20.485**

Yes

Chi - square

Degrees of freedom = 6

c) *p*-value < 0.005

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 type and area of study are not independent.

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
64
17
15
96
EN
87
43
24
154
IS
60
30
25
115
ES
70
39
45
154
Column
Total
281
129
109
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...

4.
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
60
10
26
96
EN
79
45
30
154
IS
52
34
29
115
ES
74
42
38
154
Column
Total
265
131
123...

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...

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
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...

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...

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