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 Arts & Science Allied Health Row Total Preference Business 9 40 IN 66 21 96 154 EN 82 32 IS 60 39 16 115 ES 70 40 44 154 Column Total 278 128 113 519 LAUSE 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? State the null and alternate hypotheses. O Ho: Myers-Briggs type and area of study are independent. H₁: Myers-Briggs type and area of study are not independent. OH: Myers-Briggs type and area of study are independent. H₁: Myers-Briggs type and area of study are independent. OH: Myers-Briggs type and area of study are not independent. H₁: Myers-Briggs type and area of study are independent. OH: Myers-Briggs type and area of study are not independent. H₁: Myers-Briggs type and area of study 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 Yes O No What sampling distribution will you use? O binomial O uniform O chi-square O Student's t O normal 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 < p-value < 0.100 O 0.025 a, we fail to reject the null hypothesis. O Since the P-value > a, we reject the null hypothesis. O Since the P-value sa, 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 is sufficient evidence to conclude that Myers-Briggs type and area of study are not independent. O At the 5% level of significance, there is insufficient evidence to conclude that Myers-Briggs type and area of study are not independent. 7