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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 62 professional actors, it was found that 36 were extroverts.

(a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.)

(b) Find a 95% confidence interval for p. (Round your answers to two decimal places.)

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

A random sample of 5120 permanent dwellings on an entire reservation showed that 1683 were traditional hogans.

(a) Let p be the proportion of all permanent dwellings on the entire reservation that are traditional hogans. Find a point estimate for p. (Round your answer to four decimal places.)

(b) Find a 99% confidence interval for p. (Round your answer to three decimal places.)

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

Santa Fe black-on-white is a type of pottery commonly found at archaeological excavations at a certain monument. At one excavation site a sample of 582 potsherds was found, of which 364 were identified as Santa Fe black-on-white.

(a) Let p represent the proportion of Santa Fe black-on-white potsherds at the excavation site. Find a point estimate for p. (Round your answer to four decimal places.)

(b) Find a 95% confidence interval for p. (Round your answers to three decimal places.)

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

A random sample of 5994 physicians in Colorado showed that 3251 provided at least some charity care (i.e., treated poor people at no cost).

(a) Let p represent the proportion of all Colorado physicians who provide some charity care. 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.)

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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 10,137 convicts who escaped from certain prisons, only 7582 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.)

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