Question

Giving a test to a group of students, the grades and gender are summarized below

A B C Total
Male 15 6 14 35
Female 16 18 12 46
Total 31 24 26 81

Let p represent the population proportion of all male students who received a grade of A on this test.
Use a 99% confidence interval to estimate p to four decimal places if possible.

answer ____ < p < answer ____

Answer 1

sample proportion, pcap = 15/81 = 0.1852
sample size, n = 81
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.1852 * (1 - 0.1852)/81) = 0.0432

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, Zc = Z(α/2) = 2.58

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.1852 - 2.58 * 0.0432 , 0.1852 + 2.58 * 0.0432)
CI = (0.0737 , 0.2967)

0.0737 < p < 0.2967