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 5427 physicians in Colorado showed that 3035 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=f

Answer 1

a)

sample proportion, = 3035/5427 = 0.5592

b)

sample size, n = 5427
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.5592 * (1 - 0.5592)/5427) = 0.0067

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, Zc = Z(α/2) = 2.58

Margin of Error, ME = zc * SE
ME = 2.58 * 0.0067
ME = 0.0173

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.5592 - 2.58 * 0.0067 , 0.5592 + 2.58 * 0.0067)
CI = (0.542 , 0.576)

lower limit = 0.542

Upper limit = 0.576