For this problem, carry at least four digits after the decimal in your calculati

Question

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 5643 physicians in Colorado showed that 3224 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.) lower limit upper limit Give a brief explanation of the meaning of your answer in the context of this problem. 1% of all confidence intervals 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 99% of all confidence intervals would include the true proportion of Colorado physicians providing at least some charity care. O 1% of the confidence intervals created using this method 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 n 5 Yes; np >5 and nq > 5 No; np >5 and nq 5 No; np 5.

Explanation / Answer

a) point estimate p=3224/5643=0.571

b) std error =(p(1-p)/n)1/2 =0.0066

for 99% CI ; z=2.5758

hence lower bound =point estimate - z*Std error =0.554

upper bound =point estimate + z*Std error =0.588

option 2 is correct

99% of all confidence interval created using this method.................

c)

Yes np>5 and nq>5

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