Question

The following table shows the Myers-Briggs personality preferences for a random sample of 409 people in the listed professions. Occupation Extroverted Introverted Row Total Clergy (all denominations) 65 43 108 M.D. 69 95 164 Lawyer 57 80 137 Column Total 191 218 409 Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.10 level of significance.

Answer 1

Chi-sqaure association:

H0: occupations and personality preferences are independent

Ha: occupations and personality preferences are dependent

the degree of freedom: (c-1)(r-1)= 2

c= No of columns; r= No of rows

The test statistic:

Expected value: E(x)= (Sum fo Rows* Sum of colums)/ Total

	Extoverted	Introverted	Total
Clergy	50.43521	57.56479	108
MD	76.5868	87.4132	164
Lawer	63.978	73.022	137
Total	191	218	409

P-value: 0.005

The test statistic is significant and rejects H0. There is sufficient evidence to support the claim that the listed occupations and personality preferences are independent at the 0.10 level of significance.