Question

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.
(A) 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.

(B) Referring to the scenario above, the null hypothesis will be rejected if the test statistic is ________.
(C) Referring to the scenario above, the value of the test statistic is ________.
(D) Referring to the scenario above, the p-value of the test is ________.

Answer 1

A. D

B. χ2 > 3.841

C. χ2 = 3.4806

D. 0.0621

Explanation:

Question A: 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: (d)

H0 : π1 - π2 = 0 versus H1 : π1 - π2 ≠ 0.

(B). Referring to the scenario above, the null hypothesis will be rejected if the test statistic is ________.

Answer: χ2 > 3.841

(C). Referring to the scenario above, the value of the test statistic is ________.

Answer: χ2 = 3.4806 (using the formula)

(D). Referring to the scenario above, the p-value of the test is ________.

Answer: 0.0621 (the answer could be looked up, in table)