1.

You are interested in constructing a 95% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 450 randomly selected caterpillars observed, 55 lived to become butterflies. Round answers to 4 decimal places where possible.

a. With 95% confidence the proportion of all caterpillars that lived to become a butterfly is between and .

b. If many groups of 450 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. In a recent poll, 530 people were asked if they liked dogs, and 29% said they did. Find the Margin of Error for this poll, at the 90% confidence level. Give your answer to four decimal places if possible.

3. Out of 200 people sampled, 140 had kids. Based on this, construct a 99% confidence interval for the true population proportion of people with kids.

Give your answers as decimals, to four places

4.

Assume that a sample is used to estimate a population proportion *p*. Find the 99% confidence interval for a sample of size 308 with 76% successes. Enter your answer as an **open-interval** (*i.e.*, parentheses) using decimals (not percents) accurate to three decimal places.

C.I. =

5. Assume that a sample is used to estimate a population proportion *p*. Find the 99% confidence interval for a sample of size 161 with 104 successes. Enter your answer as an **open-interval** (*i.e.*, parentheses) using decimals (not percents) accurate to three decimal places.

C.I. =

6. Express the confidence interval 0.455±0.0680.455±0.068 in open interval form (i.e., (0.155,0.855)).