Question

Problem 3

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. Problem 3 scenario, The null hypothesis will be rejected if the test statistic is greater than ____.

1. -1.96, +1.96

2. 2.706

3. -1.645, +1.645

4. 3.841

B. The value of the test statistic is_____.

1. 5.6732

2. 2.706

3. 3.841

4. 3.4806

C. The null hypothesis should be rejected.

1. True

2. False

3. Unknown

Answer 1

(A)

The test statistic under H0 follows a standard normal distribution.

Thus under a two sided hypothesis test with 5% level of significance

we reject null hypothesis if

test statistic is greater than

-1.96 , 1.96

(B)

> prop.test(x = c(65, 52), n = c(100, 100), correct = FALSE)

   2-sample test for equality of proportions without continuity correction

data: c(65, 52) out of c(100, 100)
X-squared = 3.4806, df = 1, p-value = 0.06209
alternative hypothesis: two.sided
95 percent confidence interval:
-0.005379467 0.265379467
sample estimates:
prop 1 prop 2
0.65 0.52

HENCE

The value of test statistic is

3.4806

(C)

Thus, the null hypothesis should be REJECTED

The answer is TRUE