Statistics Question

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 5778 physicians in Colorado showed that 2927 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

Answer 1

The point estimate for p is X/n: p-hat = 2927/5778 = 0.5066

We need to calculate the margin of error: E = zα/2•√[p(1 - p)/n] = 2.58•√[0.5066(0.4934)/5778] = 0.017

(0.5066 - 0.017, 0.5066 + 0.017) = (0.49, 0.524)

We are 99% confident that the proportion of all Colorado physicians who provided some charity care is between 0.49 and 0.524.