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. 61 of the 782 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 betweenand.

b.If many groups of 782 randomly selected people are surveyed, then a different confidence interval would be produced from each group. Aboutpercent 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 aboutpercent will not contain the true population proportion.

A political candidate has asked you to conduct a poll to determine what percentage of people support him. If the candidate only wants a 2% margin of error at a 99.5% confidence level, what size of sample is needed? When finding the z-value, round it to four decimal places.

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 84%. You would like to be 90% confident that your estimate is within 3.5% of the true population proportion. How large of a sample size is required?Do not round mid-calculation.

n=