Question

A psychologist is interested in constructing a 90% 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. 67 of the 849 randomly selected people who were surveyed agreed with this theory. a. With 90% 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 849 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)

n = 849, x = 67, p̅ = x/n = 0.0789  

90% Confidence interval :  

At α = 0.1, two tailed critical value, z_c = NORM.S.INV(0.1/2) =    1.645

Lower Bound = p̄ - z_c*√( p̄ *(1- p̄ )/n) = 0.0789 - 1.645 *√(0.0789*0.9211/849) =    0.064

Upper Bound = p̄ + z_c*√( p̄ *(1- p̄ )/n) = 0.0789 + 1.645 *√(0.0789*0.9211/849) =    0.094

0.064 < p < 0.094

b)

If many groups of 849 randomly selected people are surveyed, then a different confidence interval would be produced from each group. About 90 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 10 percent will not contain the true population proportion.