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)	66	41	107
M.D.	66	96	162
Lawyer	61	76	137
Column Total	193	213	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.

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 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.

(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?

Yes

No

What sampling distribution will you use?

chi-square

normal    

uniform

binomial

Student's t

What are the degrees of freedom?


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


(d) Based on your answers in parts (a) to (c), 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.

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

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

At the 5% 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 =0.05

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

b)

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	E	I	Total
	Clergy	50.865	56.135	107
	MD	77.010	84.990	162
	Lawyer	65.126	71.874	137
	total	193	213	406
chi square    χ2	=(Oi-Ei)2/Ei	E	I	Total
	Clergy	4.504	4.081	8.5847
	MD	1.574	1.426	3.0003
	Lawyer	0.261	0.237	0.4982
	total	6.3392	5.7439	12.0831
test statistic X2=		12.083

Are all the expected frequencies greater than 5? :Yes

What sampling distribution will you use? chi-square

degrees of freedom =(row-1)*(column-1)=2

c)

p value =

0.002

from excel: chidist(12.0831,2)

d)

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

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