Question

In: Statistics and Probability

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

he 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) 67 40 107
M.D. 66 96 162
Lawyer 56 81 137
Column Total 189 217 406

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.

a. H0: Myers-Briggs preference and profession are independent
b. H1: Myers-Briggs preference and profession are independent.H0: Myers-Briggs preference and profession are not independent
c. H1: Myers-Briggs preference and profession are not independent.    H0: Myers-Briggs preference and profession are not independent
d. H1: Myers-Briggs preference and profession are independent.H0: Myers-Briggs preference and profession are independent
e. 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?

a. Yes

b. No    


What sampling distribution will you use?

a. binomial

b. Student's t

c. normal

d. chi-square

e. uniform


What are the degrees of freedom?
_________________

(c) Find or estimate the P-value of the sample test statistic.

a. p-value > 0.100

b. 0.050 < p-value < 0.100    

c. 0.025 < p-value < 0.050

d. 0.010 < p-value < 0.025

e. 0.005 < p-value < 0.010

f. 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?

a. Since the P-value > α, we fail to reject the null hypothesis.

b. Since the P-value > α, we reject the null hypothesis.    

c. Since the P-value ≤ α, we reject the null hypothesis.

d. 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.    

Solutions

Expert Solution

a) level of significance =0.05

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

b)

\applying chi square test:

Expected Ei=row total*column total/grand total E I Total
Clergy 49.810 57.190 107
MD 75.414 86.586 162
Lawyer 63.776 73.224 137
total 189 217 406
chi square    χ2 =(Oi-Ei)2/Ei E I Total
Clergy 5.9322 5.1667 11.099
MD 1.1751 1.0235 2.199
Lawyer 0.9481 0.8257 1.774
total 8.055 7.016 15.071

value of the chi-square statistic =15.071

Are all the expected frequencies greater than 5? :YEs

What sampling distribution will you use? Chi square

degrees of freedom=2

c) f. p-value < 0.005

d)

c. 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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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) 58 49 107 M.D. 70 92 162 Lawyer 52 85 137 Column Total 180 226 406 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...
The following table shows the Myers-Briggs personality preferences for a random sample of 406 people in...
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