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 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 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 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?

normal

Student's t

chi-square

uniform

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. 82 77 159 Lawyer 113 99 212 Column Total 250 269 519

Explanation / Answer

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:

chi-square statistic =10.157

Are all the expected frequencies greater than 5? --Yes

What sampling distribution will you use? --- chi-square

P-value of the sample test statistic =0.006

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 Oi T F Total Clergy 55 93 148 MD 82 77 159 Lawyer 113 99 212 Total 250 269 519 Expected Ei=row*column/total T F Total Clergy 71.291 76.709 148 MD 76.590 82.410 159 Lawyer 102.119 109.881 212 Total 250 269 519 chi square =(Oi-Ei)2/Ei T F Total Clergy 3.7227 3.4598 7.182 MD 0.3822 0.3552 0.737 Lawyer 1.1593 1.0774 2.237 Total 5.264 4.892 10.157

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