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 406 people in the listed professions. E refers to extroverted and I refers to introverted.

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 not independent.     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.

(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 chi-square     Student's t binomial uniform

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 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.    

Personality Type Occupation E I Row Total Clergy (all denominations) 63 44 107 M.D. 66 96 162 Lawyer 55 82 137 Column Total 184 222 406

Explanation / Answer

a) level of significance is 5%

H0: Myers-Briggs preference and profession are independent

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

b)

Chi square test statistic is

Yes all the expected frequencies greater than 5

Chi square=10.79

c) P value= 0.004

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

e) t the 5% level of significance, there is sufficient evidence to conclude that Myers-Briggs preference and the profession are not independent.

Oi ei (oi-ei)^2/ei 63 48.4926108 4.340132 44 58.5073892 3.597227 66 73.4187192 0.749637 96 88.5812808 0.621321 55 62.08867 0.809314 82 74.91133 0.670783

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