The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day. He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors. In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors had job offers. If the accounting majors are designated as "Group 1" and the economics majors are designated as "Group 2," perform the appropriate hypothesis test using a level of significance of 0.05.
*Please note I have the solutions, but I do need further explanation for all parts.
Part A: Referring to the scenario above, the hypotheses the dean should use are:
A) H0: π1 - π2 = 0 versus H1: π1 - π2 ≠ 0.
B) H0: π1 - π2 ≠ 0 versus H1: π1 - π2 = 0.
C) H0: π1 - π2 ≤ 0 versus H1: π1 - π2 > 0.
D) H0: π1 - π2 ≥ 0 versus H1: π1 - π2 < 0.
Answer: A
Part B: Referring to the scenario above, the null hypothesis will be rejected if the test statistic is ________.
Answer: χ2 > 3.841
Part C: Referring to the scenario above, the value of the test statistic is ________.
Answer: χ2 = 3.4806 (use the formula)
Part D: Referring to the scenario above, the p-value of the test is ________.
Answer: 0.0621 (optional - this would be looked up, in table)
Part E: The managers of a company are worried about the morale of their employees. In order to determine if a problem in this area exists, they decide to evaluate the attitudes of their employees with a standardized test. They select the Fortunato test of job satisfaction, which has a known standard deviation of 24 points.
Referring to the scenario above, they should sample ________ employees if they want to estimate the mean score of the employees within 5 points with 90% confidence.