Question

The following table shows the Myers-Briggs personality preferences for a random sample of 400 people in the listed professions.

Occupation	Extroverted	Introverted	Row Total
Clergy (all denominations)	60	44	104
M.D.	70	91	161
Lawyer	54	81	135
Column Total	184	216	400

Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.01 level of significance.Find (or estimate) the P-value of the sample test statistic.

Answer 1

Null hypotheisis:Ho:   listed occupations and personality preferences are independent.

alternate hypothesis:Ha: listed occupations and personality preferences are dependent.

degree of freedom(df) =(rows-1)*(columns-1)=

for 2 df and 0.01 level of signifcance critical region       χ2=

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	Extroverted	Introverted	Total
	Clergy	47.84	56.16	104
	MD	74.06	86.94	161
	Lawyer	62.10	72.90	135
	total	184	216	400
chi square    χ2	=(Oi-Ei)2/Ei	Extroverted	Introverted	Total
	Clergy	3.0908	2.6329	5.7238
	MD	0.2226	0.1896	0.4122
	Lawyer	1.0565	0.9000	1.9565
	total	4.3699	3.7225	8.0925
test statistic X2 =		8.092
p value =		0.0175

since test statistic does not falls in rejection region we fail to reject null hypothesis

we do not have have sufficient evidence to conclude that, listed occupations and personality preferences are dependent