1.You are interested in constructing a 90% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 429 randomly selected caterpillars observed, 49 lived to become butterflies. Round answers to 4 decimal places where possible.With 90% confidence the proportion of all caterpillars that lived to become a butterfly is between__and__.b.If many groups of 429 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, 410 people were asked if they liked dogs, and 62% said they did. Find the Margin of Error for this poll, at the 99% confidence level. Give your answer to four decimal places if possible.

3.105 students at a college were asked whether they had completed their required English 101 course, and 71 students said "yes". Find the best point estimate for the proportion of students at the college who have completed their required English 101 course. Round to four decimal places.

4.Assume that a sample is used to estimate a population proportionp. Find the 80% confidence interval for a sample of size 240 with 167 successes. Enter your answer as a tri-linear inequality using decimals (not percents) accurate to three decimal places. __

4.Out of 500 people sampled, 185 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 three places __

5.Assume that a sample is used to estimate a population proportionp. Find the 99.9% confidence interval for a sample of size 81 with 56% successes. Enter your answer as anopen-interval(i.e., parentheses) using decimals (not percents) accurate to three decimal places. C.I. = ??

6.Express the confidence interval0.79 5 0.059in open interval form (i.e., (0.155,0.855)).