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.

Given statement: "The null hypothesis should be rejected" is false