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
IN | 68 | 17 | 11 | 96
EN | 87 | 40 | 27 | 154
IS | 52 | 38 | 25 | 115
ES | 70 | 44 | 40 | 154
Column Total | 277 | 139 | 103 | 519
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?
0.05
State the null and alternate hypotheses.
- H0: Myers-Briggs type and area of study are independent.
- H1: Myers-Briggs type and area of study are not independent.
- H0: Myers-Briggs type and area of study are not independent.
- H1: Myers-Briggs type and area of study are not independent.
- H0: Myers-Briggs type and area of study are not independent.
- H1: Myers-Briggs type and area of study are independent.
- 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.)