Question

The result of an accounting test was collected, and the grades and gender are summarized below

A B C Total
Male 14 15 13 42
Female 9 12  4   25
Total 23 27 17 67

Let p represent the proportion of all male students who would receive a grade of B on this test.
Use a 95% confidence interval to estimate p to three decimal places. Enter your answer as a tri-linear inequality using decimals (not percents).

answer ____ < p < answer ____

Answer 1

sample proportion, pcap = 15/67 = 0.224
sample size, n = 67
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.224 * (1 - 0.224)/67) = 0.0509

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.224 - 1.96 * 0.0509 , 0.224 + 1.96 * 0.0509)
CI = (0.124 , 0.324)

0.124 < p < 0.324