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.	72	90	162
Lawyer	57	80	137
Column Total	195	211	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 not 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 independent.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.)

What are the degrees of freedom?

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

p-value > 0.1000.050 < p-value < 0.100 0.025 < p-value < 0.0500.010 < p-value < 0.0250.005 < p-value < 0.010p-value < 0.005

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

p-value > 0.1000.050 < p-value < 0.100 0.025 < p-value < 0.0500.010 < p-value < 0.0250.005 < p-value < 0.010p-value < 0.005