The following table shows the Myers-Briggs Personality preference for a random s

Question

The following table shows the Myers-Briggs Personality preference for a random sample of 406 people in the listed professions. E refer= to extroverted and I refers to introverted Personality Type Occupation Cler M.D. Lawye Column Total 68 52 195 Row Total 07 162 137 35 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 O Ho: Myers-Briggs preference and profession are not independent H1: Myers-Briggs preference and profession are not independent. O Ho: Myers-Briggs preference and profession are independent Myers Briggs preference and profession are independent. Ho: Myers-Briggs profaranco and profassion ara not indopandant H1: Myers-Briggs preference and profession are independent. O Ho: 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? O No What sampling distribution will you use? O uniform normal O chi-square binomial Student's t What are the degrees of freedom? (c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.) (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 > a, we fail to reject the null hypothesis. Since the P-value > , we reject the null hypothesis. O Since the P-value s a, we reject the null hypothesis. O Since the P-value s a, we fail to reject the null hypothesis. (a) Interpret your conclusion in the context of the application. O At the 5% level of significance, there is insufficient evidence to conclude that Myers-Briggs preference and the profession are not independent. O At the 5% level of significance, there is sufficient evidence to conclude that Myers-Briggs preference and the profession are not independent.

Explanation / Answer

a) level of significance: =0.05

Ho: Myers-Briggs preference and profession are independent,

H1: Myers-Briggs preference and profession are not independent,

b) applying chi square test of independence:

fom above chi square value =15.222

expected frequency greater than 5 : Yes

sampling distribution: chi-square

degree of freedom =2

c) p value =0.000

d) since the p value <=alpha ; we reject the null hypothesis

e)at the 5% level of significance ; there is suffiicent evidence to conclude that ,,,,,,,,,,,,,,

Observed Oi E I Total clergy 66 41 107 MD 68 94 162 lawyer 52 85 137 Total 186 220 406 Expected Ei=row*column/total E I Total clergy 49.020 57.980 107 MD 74.217 87.783 162 lawyer 62.764 74.236 137 Total 186 220 406 chi square =(Oi-Ei)2/Ei E I Total clergy 5.8819 4.9729 10.855 MD 0.5207 0.4403 0.961 lawyer 1.8459 1.5606 3.406 Total 8.249 6.974 15.2223

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