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. 68 of the 823 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_____and ____.

b. If many groups of 823 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

n = 823, x = 68

p̄ = x/n = 0.0826

a) 99% Confidence interval :

At α = 0.01, two tailed critical value, z crit = NORM.S.INV(0.01/ 2) = 2.5758

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 0.0579 and 0.1073.

b. If many groups of 823 randomly selected people are surveyed, then a different confidence interval would be produced from each group. 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.