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.

	Personality Type
Occupation	T	F	Row Total
Clergy (all denominations)	56	92	148
M.D.	80	79	159
Lawyer	122	90	212
Column Total	258	261	519

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. State the null and alternate hypotheses. (from the following)

H₀: Myers-Briggs preference and profession are not independent.
H₁: Myers-Briggs preference and profession are not independent.

H₀: Myers-Briggs preference and profession are not independent.
H₁: Myers-Briggs preference and profession are independent.    

H₀: Myers-Briggs preference and profession are independent.
H₁: Myers-Briggs preference and profession are not independent.

H₀: Myers-Briggs preference and profession are independent.
H₁: Myers-Briggs preference and profession are independent.

C. 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.)

D. Are all the expected frequencies greater than 5?

E. What sampling distribution will you use?

F. What are the degrees of freedom?

G. Find or estimate the P-value of the sample test statistic.

H. Based on your answers in parts (a) to (g), will you reject or fail to reject the null hypothesis of independence?

Answer 1

The statistical software output for this problem is :

H₀: Myers-Briggs preference and profession are independent.
H₁: Myers-Briggs preference and profession are not independent.

C) Test statistics = 1.576

D) Yes

E ) Normal

Degrees of freedom = 2

P-value = 0.0011

reject the null hypothesis