The following table shows the Myers-Briggs personality preferences for a random

Question

The following table shows the Myers-Briggs personality preferences for a random sample of 519 people in the listed professions. T refers to thinking and F refers to feeling.

Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.01 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 or No    

What sampling distribution will you use?

Student's t

normal    

uniform

chi-square

binomial

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)


(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 > ?, we fail to reject the null hypothesis.Since the P-value > ?, we reject the null hypothesis.    Since the P-value ? ?, we reject the null hypothesis.Since the P-value ? ?, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 1% level of significance, there is insufficient evidence to conclude that Myers-Briggs preference and the profession are not independent.

At the 1% level of significance, there is sufficient evidence to conclude that Myers-Briggs preference and the profession are not independent.  

Personality Type Occupation T F Row Total Clergy (all denominations) 55 93 148 M.D. 81 78 159 Lawyer 115 97 212 Column Total 251 268 519

Explanation / Answer

Ans:

a)Level of significance=0.01

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

b)

Chi square test statistic=10.796

Yes,all the expected frequencies greater than 5.

chi-square

DF=(3-1)*(2-1)=2

c)p-value=CHIDIST(10.796,2)=0.005

d)Since the P-value ? ?, we reject the null hypothesis

e)At the 1% level of significance, there is sufficient evidence to conclude that Myers-Briggs preference and the profession are not independent.  

Observed freq.(fo) Occupation T F Row Total Clergy (all denominations) 55 93 148 M.D. 81 78 159 Lawyer 115 97 212 Column Total 251 268 519 Expected freq.(fe) Occupation T F Row Total Clergy (all denominations) 71.576 76.424 148 M.D. 76.896 82.104 159 Lawyer 102.528 109.472 212 Column Total 251 268 519 Chi square=(fo-fe)^2/fe Occupation T F Row Total Clergy (all denominations) 3.839 3.595 7.434 M.D. 0.219 0.205 0.424 Lawyer 1.517 1.421 2.938 Column Total 5.575 5.221 10.796

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