Question

In: Statistics and Probability

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) 65 42 107
M.D. 66 96 162
Lawyer 59 78 137
Column Total 190 216 406


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.

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 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.


(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?

binomial

chi-square    

Student's t

normal

uniform


What are the degrees of freedom?


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

p-value > 0.100

0.050 < p-value < 0.100    

0.025 < p-value < 0.050

0.010 < p-value < 0.025

0.005 < p-value < 0.010

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?

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

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

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

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

b)

Expected Ei=row total*column total/grand total E I Total
Clergy 50.07 56.93 107
MD 75.81 86.19 162
Lawyer 64.11 72.89 137
total 190 216 406
chi square    χ2 =(Oi-Ei)2/Ei E I Total
Clergy 4.4492 3.9136 8.363
MD 1.2701 1.1172 2.387
Lawyer 0.4078 0.3587 0.767
total 6.127 5.390 11.517

value of the chi-square statistic =11.517

Are all the expected frequencies greater than 5? :Yes

What sampling distribution will you use? :Chi square

degree of freedom(df) =(rows-1)*(columns-1)= 2

c)

p-value < 0.005

d)

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.


Related Solutions

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) 66 41 107 M.D. 73 89 162 Lawyer 52 85 137 Column Total 191 215 406 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...
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) 64 43 107 M.D. 63 99 162 Lawyer 54 83 137 Column Total 181 225 406 (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...
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) 67 40 107 M.D. 72 90 162 Lawyer 60 77 137 Column Total 199 207 406 Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.05 level of significance. (b) Find the value of...
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. 63 99 162 Lawyer 57 80 137 Column Total 178 228 406 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...
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) 66 41 107 M.D. 66 96 162 Lawyer 61 76 137 Column Total 193 213 406 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...
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...
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) 66 41 107 M.D. 71 91 162 Lawyer 61 76 137 Column Total 198 208 406 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...
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) 60 47 107 M.D. 73 89 162 Lawyer 52 85 137 Column Total 185 221 406 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...
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) 62 45 107 M.D. 69 93 162 Lawyer 57 80 137 Column Total 188 218 406 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...
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) 60 47 107 M.D. 67 95 162 Lawyer 51 86 137 Column Total 178 228 406 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...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT