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)	61	46	107
M.D.	64	98	162
Lawyer	56	81	137
Column Total	181	225	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 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 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

uniform    

normal

Student's t

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