The following table shows the Myers-Briggs personalitypreferences for a random sample of 406 people in the listedprofessions. E refers to extroverted and I refers tointroverted.

	Personality Type
Occupation	E	I	RowTotal
Clergy (all denominations)	65	42	107
M.D.	63	99	162
Lawyer	58	79	137
ColumnTotal	186	220	406

Use the chi-square test to determine if the listed occupationsand personality preferences are independent at the 0.05 level ofsignificance.

A. What is the level of significance?

B. State the null and alternate hypotheses. (from thefollowing)

H₀: Myers-Briggs preference and professionare independent
H₁: Myers-Briggs preference and profession areindependent.

H₀: Myers-Briggs preference and professionare not independent
H₁: Myers-Briggs preference and profession arenot independent.    

H₀: Myers-Briggs preference and professionare independent
H₁: Myers-Briggs preference and profession arenot independent.

H₀: Myers-Briggs preference and professionare not independent
H₁: Myers-Briggs preference and profession areindependent.

C. 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.)

D. Are all the expected frequencies greater than 5?

E. What sampling distribution will you use?

F. What are the degrees of freedom?

G. Find or estimate the P-value of the sample teststatistic.

H. Based on your answers in parts (a) to (g), will you reject orfail to reject the null hypothesis of independence?