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4. [-/5.3 Points] DETAILS BBUNDERSTAT12 10.1.014.S. MY NOTES ASK YOUR TEACHER The following table shows the Myers-Briggs personality preference and area of study for a random sample of 519 college students. In the table, IN refers to introvert, intuitive; EN refers to extrovert, intuitive; IS refers to introvert, sensing; and ES refers to extrovert, sensing Myers-Briggs Preference Arts & Science Business Allied Health Row Total 64 96 EN 79 154 55 1 15 Column Total 268 519 POup LO USE SALT Use a chi-square test to determine if Myers-Briggs preference type is independent of area of study at the 0.05 level of significance. a) What is the level of significance? End State the null and alternate hypotheses. Ho: Myers-Briggs type and area of study are independent. H,: Myers-Briggs type O Ho: Myers-Briggs type and area of study are not independent. H, : Myers-Briggs type and area of study are independent. Home O Ho: Myers-Briggs type and area of study are independent. H1: Myers-Briggs type and area of study are independent. O Ho: Myers-Briggs type and independent. H, : Myers-Briggs type and area of stu (b) Find the value of the chi-square statistic for the sample. (Round the expected frequenc cimal places. Round the test statistic to three Prison decimal places.) Are all the expected frequencies greater than 5? Yes NO What sampling distribution will you use? O binomial O' Student's t O chi-square O normal O uniform 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.) O p-value > 0.100 O 0.050 a, we fall to reject the null hypothesis. Since the P-value the null hypothesis. 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. (e) Interpret your conclusion in the context of the application. O At the 5% level of significance, there At the 5% level of signif ndependent