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. 64 of the 765 randomly selected people who were surveyed agreed with this theory. Round answers to 4 decimal places where possible.

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 between ------and .---------

b. If many groups of 765 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) Following formula can be used to calculate the confidence interval:

Given information:

p = 64/765 = 0.0836

n=765

z = 1.64 at 90% confidence interval

The confidence interval can be calculated as follows:

Therefore,

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 between 0.067 and .0.1

B)

b. If many groups of 765 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.