12.+ Question Details My Notes Ask Your Teacher For this problem, carry at least

Question

12.+ Question Details My Notes Ask Your Teacher 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 5589 physicians in Colorado showed that 3143 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 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 nclude the true proportion of Colorado hysicians pro ding at least some charity care. 1% of all confidence intervals 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. (c) Is the normal approximation to the binomial justified in this problem? Explain. Yes; np > 5 and nq> 5. No; np5 and ng>5 Yes; np

Explanation / Answer

The statistical software output for this problem is:

One sample proportion summary confidence interval:
p : Proportion of successes
Method: Standard-Wald

99% confidence interval results:

Hence,

a) p = 0.5624

b) 99% confidence interval:

Lower limit = 0.545

Upper limit = 0.579

c) Option B is correct.

d) Option A is correct.

Proportion Count Total Sample Prop. Std. Err. L. Limit U. Limit p 3143 5589 0.56235463 0.0066358911 0.5452617 0.57944755

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