For Problems 9–19, please provide the following information.

(a) What is the level of signifi­cance? State the null and alternate hypotheses.

(b) Find the value of the chi-square statistic for the sample. Are all the expected frequencies greater than 5? What sampling distribution will you use? What are the degrees of freedom?

(c) Find or estimate the P-value of the sample test statistic.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject

the null hypothesis of independence?

(e) Interpret your conclusion in the context of the application.

Use the expected values E to the hundredths place.

The following table shows the Myers–Briggs personality preference and area of study for a random sample of 519 college students (Applications of the Myers–Briggs Type Indicator in Higher Education, edited by Provost and Anchors). In the table, IN refers to introvert, intuitive; EN refers to extrovert, intuitive; IS refers to introvert, sensing; and ES refers to extrovert, sensing.

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?

Allied Health 17 30 12 37 96 Myers-Briggs Arts & Preference IN EN IS ES Column Total Science 64 82 68 75 289 Business 15 42 35 42 134 Row Total 96 154 115 154 519