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. 57 of the 708 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 708 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

Using TI 84 calculator

Press STAT then TESTS and select 1-PropZtest

x = 57

n = 708

C-level = 0.99

CALCULATE

we get

99% confidence interval = (0.0542, 0.1069)

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 0.0542 and 0.1069 .

b. If many groups of 708 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.

(this is because repated sampling for confidence interval shows that 99% confidence intervals include population proportion while 1% does not include population proportion)