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) 57 50 107 M.D. 63 99 162 Lawyer 53 84 137 Column Total 173 233 406 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 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. 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? Yes No What sampling distribution will you use? uniform Student's t chi-square normal binomial 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

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	45.594	61.406	107
	MD	69.030	92.970	162
	Lawyer	58.377	78.623	137
	total	173	233	406
chi square    χ2	=(Oi-Ei)2/Ei	E	I	Total
	Clergy	2.854	2.119	4.9724
	MD	0.527	0.391	0.9177
	Lawyer	0.495	0.368	0.8629
	total	3.8755	2.8775	6.753
test statistic X2 =		6.753

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)

0.025 < p-value < 0.050

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.