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. 52 of the 818 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 BLANK and BLANK.

b. If many groups of 818 randomly selected people are surveyed, then a different confidence interval would be produced from each group. About BLANK 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 BLANK percent will not contain the true population proportion.

Answer 1

Answer)

N = 818, P = 52/818.

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 52.

N*(1-p) = 766.

Both the conditions are met so we can use standard normal z table to estimate the interval.

Critical value z from z table for 99% confidence level is 2.576.

Margin of error (MOE) = Z*√{P*(1-P)}/√N

MOE = 0.02197515564

Interval is given by

Between P-MOE and P+MOE

Between 0.0416 and 0.0855.

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.