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 5535 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.)

lower limit
upper limit

Give a brief explanation of the meaning of your answer in the context of this problem.

We are 99% confident that the true proportion of Colorado physicians providing at least some charity care falls outside this interval.We are 99% confident that the true proportion of Colorado physicians providing at least some charity care falls within this interval.    We are 1% confident that the true proportion of Colorado physicians providing at least some charity care falls within this interval.We are 1% confident that the true proportion of Colorado physicians providing at least some charity care falls above this interval.

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

No; np < 5 and nq > 5.Yes; np > 5 and nq > 5.    Yes; np < 5 and nq < 5.No; np > 5 and nq < 5.

Answer 1

p represent the proportion of all Colorado physicians who provide some charity care (population proportion)

n = 5535 (sample size)

(a)

Number of physicians who provided at least some charity care = 2900

is the sample proportion

Answer: a point estimate for p is 0.5239

(b)

For 99% confidence interval the level of significance () = 0.01

Critical value = = = = +/- 2.576

we get this value from z table

Lower confidence interval =

Lower confidence interval = 0.507

Upper confidence interval =

Upper confidence interval = 0.541

Answer:

99% confidence interval for p :

Lower limit = 0.507

Upper limit = 0.541

Explanation of the meaning of the answer

Answer: We are 99% confident that the true proportion of Colorado physicians providing at least some charity care falls within this interval.

(c)

Answer: Yes; np > 5 and nq > 5.