4. [-15.3 Points] DETAILS BBUNDERSTAT12 10.1.0145- 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 extroy'ertl intuitive; IS refers to introvert, sensing; and ES refers to extrovert, sensing. "grzfrsefeggs Arts a Science Business Allied Health Row Total IN 69 17 10 96 EN 84 40 30 154 IS 61 30 24 115 ES 73 43 38 154 Column Total 287 130 102 519 I2 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 signicance? E State the null and alternate hypotheses. O HO: Myers-Briggs type and area of study are not independent. H1: Myers-Briggs type and area of study are independent. 0 H0: Myers-Briggs type and area of study are not independent. H1: Myers-Briggs type and area of study are not independent. 0 H0: Myers-Briggs type and area of study are independent. H1: Myers-Briggs type and area of study are not independent. 0 H0: Myers-Briggs type and area of study are independent. H1: Myers-Briggs type and area of study are 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.) E Are all the expected frequencies greater than 5? 0 Yes ONo What sampling distribution will you use? 0 chi-square 0 normal 0 binomial O uniform O Student's 1' What are the degrees of freedom? E (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 fail to reject the null hypothesis. O Since the P-value > a, we reject the null hypothesis. O 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 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