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. 68 of the 823 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 823 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 = Sample Size = 823

p = Sample Proportion = 68/823 = 0.0826

q = 1 - p = 0.9174

SE =

= 0.01

From Table, critical values of Z = 2.576

Confidence Interval:

0.0826 (2.576 X 0.009595)

= 0.0826 0.0247

=(0.0579 , 0.1073)

So,

Answer is:

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 0.0579 and 0.1073.

(b)

Answer is:

About 99.0000 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 1.0000 percent will not contain the true population proportion.