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 58 79 137 Column Total 185 221 406 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 independentH1: Myers-Briggs preference and profession are independent.H0: Myers-Briggs preference and profession are independentH1: Myers-Briggs preference and profession are independent.    H0: Myers-Briggs preference and profession are not independentH1: Myers-Briggs preference and profession are not independent.H0: Myers-Briggs preference and profession are independentH1: 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.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Chapter10: Statistics
Section10.4: Distributions Of Data
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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 58 79 137
Column Total 185 221 406

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 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 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.)
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