19

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 68 professional actors, it was found that 37 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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20.

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 5454 physicians in Colorado showed that 2900 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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Give a brief explanation of the meaning of your answer in the context of this problem.

99% of all confidence intervals would include the true proportion of Colorado physicians providing at least some charity care.

1% of the confidence intervals created using this method would include the true proportion of Colorado physicians providing at least some charity care.

99% of the confidence intervals created using this method would include the true proportion of Colorado physicians providing at least some charity care.

1% of all confidence intervals would include the true proportion of Colorado physicians providing at least some charity care.

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

Yes; np > 5 and nq > 5.

No; np < 5 and nq > 5.

Yes; np < 5 and nq < 5.

No; np > 5 and nq < 5.