Question

# The following table shows the Myers-Briggs personality preferences for a random sample of 406 people in...

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) 62 45 107 M.D. 70 92 162 Lawyer 61 76 137 Column Total 193 213 406

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 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.

(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

chi-square

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.

#### Homework Answers

Answer #1

The statistical software output for this problem is:

Hence,

a) Level of significance = 0.05

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

Option C is correct.

b) Test statistic = 6.361

Yes

chi - square

Degrees of freedom = 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.

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