Question

The following table shows the Myers-Briggs personality preferences for a random sample of 406 people in the listed professions. E refers to extroverted and I refers to introverted.

	Personality Type
Occupation	E	I	Row Total
Clergy (all denominations)	61	46	107
M.D.	71	91	162
Lawyer	54	83	137
Column Total	186	220	406

Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.05 level of significance.

(a) What is the level of significance?


State the null and alternate hypotheses.

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

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

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

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

(b) 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.)


Are all the expected frequencies greater than 5?

A) Yes

B) No     

What sampling distribution will you use?

A) uniform

B) binomial     normal

C) Student's t

D) chi-square

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample test statistic.

A) p-value > 0.100

B) 0.050 < p-value < 0.100     0.025 < p-value < 0.050

C) 0.010 < p-value < 0.025

D) 0.005 < p-value < 0.010

E) p-value < 0.005

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

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

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

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

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

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

A) At the 5% level of significance, there is insufficient evidence to conclude that Myers-Briggs preference and the profession are not independent

B) At the 5% level of significance, there is sufficient evidence to conclude that Myers-Briggs preference and the profession are not independent.   

Answer 1

Observed
	E	I	total
clergy	61	46	107
MD	71	91	162
Lawyer	54	83	137
Total	186	220	406

Ei = sum(rowi)*sum(coli)/total

Expected
	E	I
clergy	49.020	57.980
MD	74.217	87.783
Lawyer	62.764	74.236

chi-square = sum((Oi - Ei)^2/Ei)

a)
0.05,

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

b)
test statistic,
chi-square = 7.919

yes

chi-square

df = 2

0.019
0.010 < p-value < 0.025

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

At the 5% level of significance, there is insufficient evidence to conclude that Myers-Briggs preference and the profession are not independent