For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.Case studies showed that out of 10,341 convicts who escaped from certain prisons, only 7770 were recaptured. (a) Let p represent the proportion of all escaped convicts who will eventually be recaptured. Find a point estimate for p. (Round your answer to four decimal places.)  (b) Find a 99% confidence interval for p. (Round your answers to three decimal places.) lower limit       upper limit

You are interested in constructing a 90% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 377 randomly selected caterpillars observed, 42 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 377 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.

You are interested in constructing a 90% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 378 randomly selected caterpillars observed, 45 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 378 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.

Tina catches a 14-pound bass.  She does not know the population mean or standard deviation.  So she takes a sample of five friends and they say the last bass they caught was 9, 12, 13, 10, and 10 pounds.  Find the t and calculate a 95% (α = .05) confidence interval.