Psychology: Myers-Briggs The following table shows the Myers-Briggs personality

Question

Psychology: Myers-Briggs The following table shows the Myers-Briggs personality preference and professions for a random sample of 2408 people in the listed professions (Atlas of Type Tables, by Macdaid, McCaulley, and Kainz). E refers to extroverted, and I refers to introverted. (a) Conduct a test to determine if the listed occupations and personality preferences are independent at the 1% level of significance. b) What is the probability that a person is an MD and Extrovert? c) What is the probability that a person is a lawyer? d) What is the probability that a person is an Extrovert given an MD? e) What is the probability that a person is an MD given an Extrovert? f) Most people claim most doctors do not have good bed side manners. Test to determine of part of this reason is due to their personality preference. Perform a test using P(MD/Extrovert) and P(MD/Introvert) to determine if more doctors are introverts.

Explanation / Answer

Question a)

Here we use Chi-square test of independence:

Oi = Observed Frequency

Ei = Expected Frequency

X^2 = sum of (Oi – Ei)^2 / Ei

Null and Alternative Hypothesis:

H0: Occupations and personality preferences are independent.

H1: Occupations and personality preferences are dependent.

Oi are the given values

Ei = (Row total *Colum total )/Total

Oi:

E

I

Row Total

Clergy

308

226

534

M.D.

667

936

1603

Lawyer

112

159

271

Column Total

1087

1321

2408

Ei:

241.053987

292.946013

723.613372

879.386628

122.332641

148.667359

Oi – Ei:

66.946013

-66.946013

-56.613372

56.613372

-10.332641

10.332641

(Oi – Ei)^2:

4481.7687

4481.7687

3205.0739

3205.0739

106.7635

106.7635

(Oi –Ei)^2/Ei:

18.592

15.299

4.429

3.645

0.873

0.718

X^2 = 43.556

Now for (3-1)*(2-1) = 2 degrees of freedom at 1% level of significance the critical X^2 is given as 9.210

The value of calculated chi-square is greater than the critical chi-square value (43.556 > 9.210); we reject the null hypothesis.

At 1% level of significance there is not sufficient evidence to conclude that listed occupations and personality preferences are independent.

Question b)

P ( MD and Extrovert) = 667/2408

                                        = 0.2770

Answer: 0.2770

Question c)

P (person is a lawyer) = 271 / 2408

                                         = 0.1125

Answer: 0.1125

Question d)

P ( extrovert| given MD) = 667 / 1603

                                              = 0.4161

Answer: 0.4161

E

I

Row Total

Clergy

308

226

534

M.D.

667

936

1603

Lawyer

112

159

271

Column Total

1087

1321

2408

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