5. [-/0.27 Points] DETAILS 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) 63 44 107 M.D 73 89 162 Lawyer 59 78 137 Column Total 195 211 406 LA USE SALT 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. Ho: Myers-Briggs preference and profession are not independent H1: Myers-Briggs preference and profession are independent. Ho: Myers-Briggs preference and profession are independent H1: Myers-Briggs preference and profession are independent. Ho: Myers-Briggs preference and profession are independent H1: Myers-Briggs preference and profession are not independent. Ho: Myers-Briggs preference and profession are not 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? Yes No What sampling distribution will you use? binomial normal chi-square uniform Student's t What are the degrees of freedom? (c) Find or estimate the P-value of the sample test statistic. p-value > 0.100 0.050