21) 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 10,494 convicts who escaped from certain prisons, only 7911 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

Give a brief statement of the meaning of the confidence interval.

a. 99% of all confidence intervals would include the true proportion of recaptured escaped convicts.

b. 99% of the confidence intervals created using this method would include the true proportion of recaptured escaped convicts.

c. 1% of the confidence intervals created using this method would include the true proportion of recaptured escaped convicts.

d. 1% of all confidence intervals would include the true proportion of recaptured escaped convicts.

(c) Is use of the normal approximation to the binomial justified in this problem? Explain.

a. No; np < 5 and nq > 5.

b. No; np > 5 and nq < 5.

c.Yes; np < 5 and nq < 5.

d. Yes; np > 5 and nq > 5.

22) For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a combined study of northern pike, cutthroat trout, rainbow trout, and lake trout, it was found that 40 out of 857 fish died when caught and released using barbless hooks on flies or lures. All hooks were removed from the fish.

(a) Let p represent the proportion of all pike and trout that die (i.e., p is the mortality rate) when caught and released using barbless hooks. 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

Give a brief explanation of the meaning of the interval.

a.99% of all confidence intervals would include the true catch-and-release mortality rate.

b. 1% of the confidence intervals created using this method would include the true catch-and-release mortality rate.

c. 1% of all confidence intervals would include the true catch-and-release mortality rate.

d. 99% of the confidence intervals created using this method would include the true catch-and-release mortality rate.

(c) Is the normal approximation to the binomial justified in this problem? Explain.

a. No; np > 5 and nq < 5.

b. Yes; np < 5 and nq < 5.

c. Yes; np > 5 and nq > 5.

d. No; np < 5 and nq > 5.