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)	67	40	107
M.D.	73	89	162
Lawyer	55	82	137
ColumnTotal	195	211	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?


State the null and alternate hypotheses.

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

(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?

YesNo    

What sampling distribution will you use?

Student'stuniform    chi-squarenormalbinomial

What are the degrees of freedom?


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

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

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

Since the P-value > α, we fail to rejectthe null hypothesis.Since the P-value > α, wereject the null hypothesis.    Since theP-value ≤ α, we reject the null hypothesis.Sincethe P-value ≤ α, we fail to reject the nullhypothesis.

(e) Interpret your conclusion in the context of theapplication.

At the 5% level of significance, there is insufficient evidenceto conclude that Myers-Briggs preference and the profession are notindependent.At the 5% level of significance, there is sufficientevidence to conclude that Myers-Briggs preference and theprofession are not independent.