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.	73	89	162
Lawyer	52	85	137
Column Total	191	215	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 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 not independent. H₀: Myers-Briggs preference and profession are 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?

Student's t chi-square     binomial normal uniform

What are the degrees of freedom?


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

p-value > 0.100 0.050 < p-value < 0.100     0.025 < p-value < 0.050 0.010 < p-value < 0.025 0.005 < p-value < 0.010 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?

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

Ans:

a)level of significance=0.05

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

	Observed(fo)
Occupation	E	I	Row Total
Clergy	66	41	107
M.D.	73	89	162
Lawyer	52	85	137
Column Total	191	215	406
	Expecetd(fe)
Occupation	E	I	Row Total
Clergy	50.34	56.66	107
M.D.	76.21	85.79	162
Lawyer	64.45	72.55	137
Column Total	191	215	406
	Chi square=(fo-fe)^2/fe
Occupation	E	I	Row Total
Clergy	4.873	4.329	9.203
M.D.	0.135	0.120	0.256
Lawyer	2.405	2.137	4.542
Column Total	7.414	6.586	14.000

b)Test statistic:

Chi square=14.000

Yes, all the expected frequencies greater than 5.

chi-square  

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

c)p-value=chidist(14.000,2)=0.0009

p-value < 0.005

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.