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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 Row Total Clergy (all denominations) 59 M.D. 63 99 Lawyer 61 76 Column Total 183 223 LO 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 Enter a number. e level of significance? 0.05 State the null and alternate hypotheses. O Ho: Myers-Briggs preference and profession are not independent H,: Myers-Briggs preference and ndent. O Ho: Myers-Briggs prefe ndependent H, : Myers-Briggs pref independent. End O Ho: Myers-Briggs preference and ssion are independent H. : Myers-Briggs preferer sion are not independent. O Ho: Myers-Briggs preferen sion are not independent H, : Myers-Briggs preference and profession are not independent. Home (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 Prison What sampling distribution will you use? O normal chi-square binomial uniform Student's t What are the degrees of freedom? (c) Find or estimate the P-value of the sample test statistic, O p-value > 0.100 O 0.050 a, we fail to reject the null hypothesis. O Since the P-value > O Since the P-value S a, we reject the null hypothesis. Since the P-value S a, we fail to reject the null hypothesis. e) Interpret your conclusion in the context of the application. O At the 5% level of significance, there is At the 5% level of signifi dependent