1. You are interested in constructing a 90% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 355 randomly selected caterpillars observed, 48 lived to become butterflies. Round answers to 4 decimal places where possible.

a. With 90% confidence the proportion of all caterpillars that lived to become a butterfly is between_____ and _____.

b. If many groups of 355 randomly selected caterpillars were observed, then a different confidence interval would be produced from each group. About______ percent of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about ________ percent will not contain the true population proportion.

2. A political candidate has asked you to conduct a poll to determine what percentage of people support him. If the candidate only wants a 1% margin of error at a 99% confidence level, what size of sample is needed? When finding the z-value, round it to four decimal places.

Answer: _________

3. You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately =40.6=40.6. You would like to be 90% confident that your estimate is within 3 of the true population mean. How large of a sample size is required? n = _____________