1 We wish to estimate what percent of adult residents in a certain county are parents. Out of 200 adult residents sampled, 178 had kids. Based on this, construct a 90% confidence interval for the proportion p of adult residents who are parents in this county.Express your answer in tri-inequality form. Give your answers as decimals, to three places. < p < Express the same answer using the point estimate and margin of error. Give your answers as decimals, to three places.
2. You are interested in constructing a 95% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 390 randomly selected caterpillars observed, 56 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 390 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.3. A newsgroup is interested in constructing a 99% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 605 randomly selected Americans surveyed, 439 were in favor of the initiative. Round answers to 2 decimal places where possible.
a. With 99% confidence the proportion of all Americans who favor the new Green initiative is between and .
b. If many groups of 605 randomly selected Americans were 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 Americans who favor the Green initiative and about percent will not contain the true population proportion.
