Question

The office of records at a university has stated that the proportion of incoming female students who major in business has increased. A random sample of female students selected several years ago is compared with a random sample of female students selected this year. Results are summarized below. Has the proportion increased significantly? Test at α = .10.

	Sample Size	No. Majoring in Business
Previous sample	250	50
Present sample	300	69

Answer 1

p1cap = X1/N1 = 50/250 = 0.2
p1cap = X2/N2 = 69/300 = 0.23
pcap = (X1 + X2)/(N1 + N2) = (50+69)/(250+300) = 0.2164

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 < p2

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.2-0.23)/sqrt(0.2164*(1-0.2164)*(1/250 + 1/300))
z = -0.85

P-value Approach
P-value = 0.1977

As P-value >= 0.1, fail to reject null hypothesis.

There is not sufficient evidence to conclude that the proportion has increased significantly