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. 56 of the 754 randomly selected people who were surveyed agreed with this theory.

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 754 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

Solution :

Given that,

Point estimate = sample proportion = = x / n = 56 / 754 = 0.0743

1 - = 1 - 0.0743 = 0.9257

Z/2 = Z0.005 = 2.576

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 2.576 (((0.0743 * 0.9257) / 754)

= 0.0246

A 99% confidence interval for population proportion p is ,

± E  

= 0.0743  ± 0.0246

= ( 0.0497, 0.0989 )

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 0.0497 and 0.0989.

b. If many groups of 754 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.