The following table shows the Myers-Briggs personality preferences for a random
ID: 3228969 • Letter: T
Question
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.
H0: Myers-Briggs preference and profession are independent.
H1: Myers-Briggs preference and profession are not independent.
All the expected frequencies are greater than 5.
Chi-square sampling distribution.
Since the P-value , we reject the null hypothesis.
At the 1% level of significance, there is sufficient evidence to conclude that Myers-Briggs preference and the profession are not independent.
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 of significance? _______________
(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.)_______________
(c) What are the degrees of freedom?_______________
(d) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)_______________
Personality Type Occupation T F Row Total Clergy (all denominations) 54 94 148 M.D. 79 80 159 Lawyer 114 98 212 Column Total 247 272 519Explanation / Answer
(a) The level of significance=0.01
(b) The value of the chi-square statistic for the sample=10.846
(c) The degrees of freedom=2_______________
(d) The P-value of the sample test statistic=0.004
As p-value<0.01, we reject the null hypothesis and conclude that Myers-Briggs preference and profession are not independent.
Chi-Square Test
Observed Frequencies
Personality Type
Calculations
Occupation
T
F
Total
fo-fe
Clergy
54
94
148
-16.4355
16.43545
MD
79
80
159
3.32948
-3.32948
Lawyer
114
98
212
13.10597
-13.106
Total
247
272
519
Expected Frequencies
Personality Type
Occupation
T
F
Total
(fo-fe)^2/fe
Clergy
70.435
77.565
148
3.835059
3.482572
MD
75.671
83.329
159
0.146496
0.133031
Lawyer
100.894
111.106
212
1.702445
1.54597
Total
247
272
519
Data
Level of Significance
0.01
Number of Rows
3
Number of Columns
2
Degrees of Freedom
2
Results
Critical Value
9.210
Chi-Square Test Statistic
10.846
p-Value
0.004
Reject the null hypothesis
Expected frequency assumption
is met.
Chi-Square Test
Observed Frequencies
Personality Type
Calculations
Occupation
T
F
Total
fo-fe
Clergy
54
94
148
-16.4355
16.43545
MD
79
80
159
3.32948
-3.32948
Lawyer
114
98
212
13.10597
-13.106
Total
247
272
519
Expected Frequencies
Personality Type
Occupation
T
F
Total
(fo-fe)^2/fe
Clergy
70.435
77.565
148
3.835059
3.482572
MD
75.671
83.329
159
0.146496
0.133031
Lawyer
100.894
111.106
212
1.702445
1.54597
Total
247
272
519
Data
Level of Significance
0.01
Number of Rows
3
Number of Columns
2
Degrees of Freedom
2
Results
Critical Value
9.210
Chi-Square Test Statistic
10.846
p-Value
0.004
Reject the null hypothesis
Expected frequency assumption
is met.
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