Question

professions. T refers to thinking and F refers to feeling.

	Personality Type
Occupation	T	F	Row Total
Clergy (all denominations)	60	88	148
M.D.	72	87	159
Lawyer	123	89	212
Column Total	255	264	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 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 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?

YesNo    

What sampling distribution will you use?

chi-squarenormal    uniformbinomialStudent's t

What are the degrees of freedom?


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

p-value > 0.1000.050 < p-value < 0.100    0.025 < p-value < 0.0500.010 < p-value < 0.0250.005 < p-value < 0.010p-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?

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 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:

Expected	Ei=row total*column total/grand total	T	F	Total
	Clergy	72.72	75.28	148
	M.D.	78.12	80.88	159
	Lawyer	104.16	107.84	212
	total	255	264	519
chi square    χ2	=(Oi-Ei)2/Ei	T	F	Total
	Clergy	2.2239	2.1481	4.372
	M.D.	0.4797	0.4633	0.943
	Lawyer	3.4070	3.2908	6.698
	total	6.111	5.902	12.013

value of the chi-square statistic =12.013

Are all the expected frequencies greater than 5? Yes

What sampling distribution will you use? chi square

degrees of freedom? =3

c)

0.005 <p-value < 0.010

d)

Since the P-value ≤ α, 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.