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.

Determine whether the following is true or false: The null hypothesis should be rejected.

Please explain in detail.

Answer #1

Below are the null and alternative Hypothesis,

Null Hypothesis, H0: p1 = p2

Alternate Hypothesis, Ha: p1 ≠ p2

p1cap = X1/N1 = 65/100 = 0.65

p1cap = X2/N2 = 52/100 = 0.52

pcap = (X1 + X2)/(N1 + N2) = (65+52)/(100+100) = 0.585

Test statistic

z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))

z = (0.65-0.52)/sqrt(0.585*(1-0.585)*(1/100 + 1/100))

z = 1.87

P-value Approach

P-value = 0.0615

As P-value >= 0.05, fail to reject null hypothesis.

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