Question

A psychologist is interested in constructing a 99% confidence interval for the proportion of people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain. 63 of the 793 randomly selected people who were surveyed agreed with this theory. Round answers to 4 decimal places where possible.

a. With 99% confidence the proportion of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain is between answer  _____ and answers ________.

b. If many groups of 793 randomly selected people are surveyed, then a different confidence interval would be produced from each group. About answer _______ percent of these confidence intervals will contain the true population proportion of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain and about answer ________ percent will not contain the true population proportion.

Answer 1

sample proportion, pcap = 63/793 = 0.0794
sample size, n = 793
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.0794 * (1 - 0.0794)/793) = 0.0096

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 = (0.0794 - 2.58 * 0.0096 , 0.0794 + 2.58 * 0.0096)
CI = (0.0546 , 0.1042)

With 99% confidence the proportion of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain is between 0.0546 and 0.1042

b)
About 99 percent of these confidence intervals will contain the true population proportion of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain and about 1 percent will not contain the true population proportion.