Question

Question 21

Question text

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

Occupation	Extroverted	Introverted	Row Total
Clergy (all denominations)	62	42	104
M.D.	70	95	165
Lawyer	56	81	137
Column Total	188	218	406

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Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.05 level of significance. Given P-Value < 0.005, will you reject or fail to reject the null hypothesis of independence?

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Select one:

a. Since the P-value is less than α, we reject the null hypothesis that the Myers-Briggs personality preference and profession are independent. At 0.05 level of significance, we conclude that the Myers-Briggs personality preference and profession are not independent.

b. Since the P-value is greater than α, we fail to reject the null hypothesis that the Myers-Briggs personality preference and profession are not independent. At 0.05 level of significance, we conclude that the Myers-Briggs personality preference and profession are independent.

c. Since the P-value is greater than α, we reject the null hypothesis that the Myers-Briggs personality preference and profession are independent. At 0.05 level of significance, we conclude that the Myers-Briggs personality preference and profession are not independent.

d. Since the P-value is greater than α, we reject the null hypothesis that the Myers-Briggs personality preference and profession are not independent. At 0.05 level of significance, we conclude that the Myers-Briggs personality preference and profession are independent.

e. Since the P-value is less than α, we reject the null hypothesis that the Myers-Briggs personality preference and profession are not independent. At 0.05 level of significance, we conclude that the Myers-Briggs personality preference and profession are independent.

Question 25

Question text

The following table shows the Myers-Briggs personality preferences for a random sample of 409 people in the listed professions.

Occupation	Extroverted	Introverted	Row Total
Clergy (all denominations)	65	43	108
M.D.	69	95	164
Lawyer	57	80	137
Column Total	191	218	409

Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.10 level of significance. Depending on the P-value, will you reject or fail to reject the null hypothesis of independence?

Select one:

a. Since the P-value is greater than α, we fail to reject the null hypothesis that the Myers-Briggs personality preference and profession are independent. At 0.10 level of significance, we conclude that the Myers-Briggs personality preference and profession are not independent.

b. Since the P-value is greater than α, we reject the null hypothesis that the Myers-Briggs personality preference and profession are not independent. At 0.10 level of significance, we conclude that the Myers-Briggs personality preference and profession are independent.

c. Since the P-value is greater than α, we fail to reject the null hypothesis that the Myers-Briggs personality preference and profession are not independent. At 0.10 level of significance, we conclude that the Myers-Briggs personality preference and profession are independent.

d. Since the P-value is less than α, we reject the null hypothesis that the Myers-Briggs personality preference and profession are independent. At 0.10 level of significance, we conclude that the Myers-Briggs personality preference and profession are not independent.

e. Since the P-value is less than α, we fail to reject the null hypothesis that the Myers-Briggs personality preference and profession are independent. At 0.10 level of significance, we conclude that the Myers-Briggs personality preference and profession are not independent.

Answer 1

Question 21

Answer : Option ( a )

Since the P-value is less than α, we reject the null hypothesis that the Myers-Briggs personality preference and profession are independent. At 0.05 level of significance, we conclude that the Myers-Briggs personality preference and profession are not independent.

Question 25

Answer : Option ( d )

Since the P-value is less than α, we reject the null hypothesis that the Myers-Briggs personality preference and profession are independent. At 0.10 level of significance, we conclude that the Myers-Briggs personality preference and profession are not independent

Explanation

	Column 1	Column 2	Total
Row 1	65	43	108
Row 2	69	95	164
Row 3	57	80	137
Total	191	218	409

Expected Values	Column 1	Column 2	Total
Row 1	191*108/409 = 50.435	218*108/409 = 57.565	108
Row 2	191*164/409 = 76.587	218*164/409 = 87.413	164
Row 3	191*137/409 = 63.978	218*137/409 = 73.022	137
Total	191	218	409

P value :

with chi score = 10.729 , d f = 2

we get p value = .00468.

Decision

p value < L.o.s

i.e 0 00468. < 0.10

so reject H₀