For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. In a random sample of 64 professional actors, it was found that 44 were extroverts.   (a) Let p represent the proportion of all actors who are extroverts. Find point estimates for p and q. (Round your answer to four decimal places.) p̂=q̂= (b) Find a 95% confidence interval for p. Find the maximal margin of error. (Round your answer to two decimal places.) E =  Report the bounds from the 95% confidence interval for p. (Round your answers to two decimal places.) lower limitupper 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.

A College Alcohol Study interviewed an SRS of 1000 college students about their drinking habits. Suppose that half of all college students "drink to get drunk" at least once in a while. That is sample proportion, p-hat 0.5. %3D 9. Estimate a 95% confidence interval for the actual percentage among all students. Round the number to nearest hundredth. O47% to 53% O 50% to 55% 43% to 52% O 44% to 56%

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.