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 70 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 = c) Report the bounds from the 95% confidence interval for p. (Round your answers to two 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 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.

If n=17, (x-bar)=48, and s=2, construct a confidence interval at a 80% confidence level. Assume the data came from a normally distributed population. Give your answers to one decimal place.

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, 60 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.

Thelma and Louise are each attempting to estimate the proportion of adults who enjoy listening to country music. They each survey a different random sample of adults, and in each sample, the proportion who say they enjoy listening to country music is 0.29. Thelma and Louise each use their sample data to construct a confidence interval. Thelma's interval is from 0.242 to 0.338 and Louise's interval is from 0.237 to 0.323. One of these intervals was computed correctly and the other was not. Which interval must be the correct one? It's impossible to answer this question without knowing the level of confidence used for each interval. It's impossible to answer this question without knowing the sample sizes. O It's impossible to answer this question without knowing the sample sizes or the level of confidence used for each interval. Thelma's interval must be the correct interval. O Louise's interval must be the correct interval.

Answer Part B

The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught. Step 2 of 2 :  Suppose a sample of 716 suspected criminals is drawn. Of these people, 286 were captured. Using the data, construct the 90% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list. Round your answers to three decimal places.   EXCEL FORMULAS IF YOU HAVE IT PLEASE EXPLAIN IT ALSO

You are interested in constructing a 99% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 418 randomly selected caterpillars observed, 59 lived to become butterflies. Round answers to 4 decimal places where possible. a.  With 99% confidence the proportion of all caterpillars that lived to become a butterfly is between and . b.  If many groups of 418 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.