Question

What percentage of hospitals provide at least some charity care? Based on a random sample of hospital reports from eastern states, the following information is obtained (units in percentage of hospitals providing at least some charity care): 56.5 55.8 52.9 66 59.0 64.7 70.1 64.7 53.5 78.2 Assume that the population of x values has an approximately normal distribution. (a) Use a calculator with mean and sample standard deviation keys to find the sample mean percentage x and the sample standard deviation s. (Round your answers to one decimal place.) x = % s = % (b) Find a 90% confidence interval for the population average μ of the percentage of hospitals providing at least some charity care. (Round your answers to one decimal place.) lower limit % upper limit %

Answer 1

a)

sample mean, xbar = 62.1%
sample standard deviation, s = 8.1%

b)

sample size, n = 10
degrees of freedom, df = n - 1 = 9

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 1.83

ME = tc * s/sqrt(n)
ME = 1.83 * 8.1/sqrt(10)
ME = 4.687

CI = (62.1 - 1.83 * 8.1/sqrt(10) , 62.1 + 1.83 * 8.1/sqrt(10))
CI = (57.4 , 66.8)

Lower limit = 57.4%
Upper limit = 66.8%