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 5940 physicians in Colorado showed that 3332 provided at least some charity care (ie, 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.) 5609 (b) Find a 99% confidence interval for p. (Round your answers to three decimal places.) lower limit 549 upper limit 573 Give a brief explanation of the meaning of your answer in the context of this problem. G 1% of the confidence intervals created using this method would include the true proportion of Colorado physicians providng at least some chary are 99% of the confidence intervals created using this method would nclude the true proportion of Colorado physicans proving at least some chanty are. 1% or ali confidence intervals would indude the true proportion of Colorado physicians providng at least some chanty care. 99% of all confidence intervals would include the true proportion of Colorado physicians providing at least some charity are (e) Is the normal approximation to the binomial Justiried in this problem? Explain No; np 5 and nq

Explanation / Answer

b)

p = 3332/5940 = 0.561 , n =5940

z value at 99% CI = 2.576

CI = p +/- z * sqrt(p*(1 - p) / n))
= 0.561 +/- 2.576 * sqrt ( 0.561 * 0.439 / 5940)
= (0.544 , 0.577)
Upper limit = 0.544
Lower limit = 0.577

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