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.	79	80	159
Lawyer	118	94	212
Column Total	253	266	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?


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 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.

(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 > ?, we fail to reject the null hypothesis.

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

Since the P-value ? ?, we reject the null hypothesis.

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

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

b)

applying chi square test of independence:

Observed	OBS	T	F	Total
	Clergy	56	92	148
	MD	79	80	159
	Lawyer	118	94	212
	Total	253	266	519
Expected	Ei=?row*?column/?total	T	F	Total
	Clergy	72.146	75.854	148
	MD	77.509	81.491	159
	Lawyer	103.345	108.655	212
	Total	253	266	519
chi square	=(Oi-Ei)2/Ei	T	F	Total
	Clergy	3.61	3.44	7.05
	MD	0.03	0.027	0.06
	Lawyer	2.08	1.977	4.05
	Total	5.72	5.44	11.161

  chi-square statistic =11.161

expected frequencies greater than 5 --Yes

sampling distribution will you use-chi square

degrees of freedom =(row-1)*(column-1)=(3-1)*(2-1)=2

c)

p value =0.004

d)

Since the P-value ? ?, we reject the null hypothesis.

e)

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