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. Personality Type Occupation E I Row Total Clergy (all denominations) 61 46 107 M.D. 66 96 162 Lawyer 52 85 137 Column Total 179 227 406 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 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? chi-square Student's t normal binomial 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 > ð›¼, 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.

          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)   61   46   107
M.D.   66   96   162
Lawyer   52   85   137
Column Total   179   227   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 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?
chi-square
Student's t
normal
binomial
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 > ð›¼, 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.

Added by Ivan H.

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