Please show all work The contingency table below shows the M

Please show all work

The contingency table below shows the Myers-Briggs personality preferences for a random sample of 401 people in the listed professions.

Occupation

Extroverted

Introverted

Row Total

Clergy (all denominations)

60

48

108

M.D.

65

94

159

Lawyer

54

80

134

Column Total

179

222

401

Find the degrees of freedom using the formula df = (r-1)(c-1)

Occupation	Extroverted	Introverted	Row Total
Clergy (all denominations)	60	48	108
M.D.	65	94	159
Lawyer	54	80	134
Column Total	179	222	401

Solution

The contingency table below shows the Myers-Briggs personality preferences for a random sample of 401 people in the listed professions.

Use the chi-square test to determine if the listed occupations and personality preferences are independent at

Null hypothesis: occupations and personality preferences are independent

Alternate hypothesis: occupations and personality preferences are not independent

degrees of freedom using the formula df = (r-1)(c-1) = (3-1)(2-1) =2

If the chi-square test statistic is do we reject the null hypothesis or fail to reject the null hypothesis at the 0.05 significance level?

Table value of chi square at 0.05 level for 2 DF =5.991

Calculated chi square =7.139 > 5.991 the table value.

The null hypothesis is rejected

We conclude that occupations and personality preferences are not independent.

Chi-Square Test

Observed Frequencies

Column variable

Calculations

Extroverted

Introverted

Total

fo-fe

Clergy

60

48

108

11.7905

-11.7905

M.D.

65

94

159

-5.9751

5.9751

Lawyer

54

80

134

-5.8155

5.8155

Total

179

222

401

Expected Frequencies

Column variable

Extroverted

Introverted

Total

(fo-fe)^2/fe

Clergy

48.20948

59.79052

108

2.8836

2.3251

M.D.

70.97506

88.02494

159

0.5030

0.4056

Lawyer

59.81546

74.18454

134

0.5654

0.4559

Total

179

222

401

Data

Level of Significance

0.05

Number of Rows

3

Number of Columns

2

Degrees of Freedom

2

Results

Critical Value

5.991

Chi-Square Test Statistic

7.139

p-Value

0.0282

Reject the null hypothesis

Chi-Square Test
Observed Frequencies
	Column variable			Calculations
	Extroverted	Introverted	Total		fo-fe
Clergy	60	48	108		11.7905	-11.7905
M.D.	65	94	159		-5.9751	5.9751
Lawyer	54	80	134		-5.8155	5.8155
Total	179	222	401
Expected Frequencies
	Column variable
	Extroverted	Introverted	Total		(fo-fe)^2/fe
Clergy	48.20948	59.79052	108		2.8836	2.3251
M.D.	70.97506	88.02494	159		0.5030	0.4056
Lawyer	59.81546	74.18454	134		0.5654	0.4559
Total	179	222	401
Data
Level of Significance	0.05
Number of Rows	3
Number of Columns	2
Degrees of Freedom	2
Results
Critical Value	5.991
Chi-Square Test Statistic	7.139
p-Value	0.0282
Reject the null hypothesis