Question

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A psychologist is interested in constructing a 95% 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. 59 of the 703 randomly selected people who were surveyed agreed with this theory.

a. With 95% 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 betweenand .

b. If many groups of 703 randomly selected people are surveyed, then a different confidence interval would be produced from each group. About  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  percent will not contain the true population proportion.

Answer 1

a)
sample proportion, = 0.0839
sample size, n = 703
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.0839 * (1 - 0.0839)/703) = 0.01

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

Margin of Error, ME = zc * SE
ME = 1.96 * 0.01
ME = 0.0196

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.0839 - 1.96 * 0.01 , 0.0839 + 1.96 * 0.01)
CI = (0.0643 , 0.1035)

. With 95% 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 0.0643 and 0.1035

b)

If many groups of 703 randomly selected people are surveyed, then a different confidence interval would be produced from each group. About 95 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 5 percent will not contain the true population proportion.