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)	52	96	148
M.D.	78	81	159
Lawyer	122	90	212
Column Total	252	267	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:

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

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 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.

(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? (Yes/No)

(E) What sampling distribution will you use? (uniform / Student's t / chi-square / binomial / normal)

(F) What are the degrees of freedom?

(G) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

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

Since the P-value > α, we fail to reject the null hypothesis.

Since the P-value > α, we reject the null hypothesis.    

Since the P-value ≤ α, we reject the null hypothesis.

Since the P-value ≤ α, we fail to reject the null hypothesis.

(I) Interpret your conclusion in the context of the application.

At the 1% level of significance, there is insufficient evidence to conclude that Myers-Briggs preference and the profession are not independent.

At the 1% level of significance, there is sufficient evidence to conclude that Myers-Briggs preference and the profession are not independent.    

Answer 1

A)

level of significance =0.01

B)

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

C)

Applying chi square test:

Expected	Ei=row total*column total/grand total	A	C	Total
	Clergy	71.86	76.14	148
	M.D.	77.20	81.80	159
	Lawyer	102.94	109.06	212
	total	252	267	519
chi square    χ2	=(Oi-Ei)2/Ei	A	C	Total
	Clergy	5.4893	5.1809	10.670
	M.D.	0.0082	0.0078	0.016
	Lawyer	3.5305	3.3322	6.863
	total	9.028	8.521	17.5490

value of the chi-square statistic for the sample =17.549

D)Yes

E) chi-square

F) degrees of freedom =2

G) p value =0.000

H)

Since the P-value ≤ α, we reject the null hypothesis.

I)

At the 1% level of significance, there is sufficient evidence to conclude that Myers-Briggs preference and the profession are not independent.