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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 247 272 519

Explanation / 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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