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

[shortposting]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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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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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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