Question

A simple random sample of 101 cities and counties in the United States was selected and the number of positive COVID-19 cases per 1000 citizens was recorded for each. The mean number of positive cases for this sample of 101 counties and cities was 253, with a standard deviation of 11.4. Use this information to calculate and interpret a 99% confidence interval for the mean number of positive COVID-19 cases per 1000 citizens for all counties and cities in the United States

Answer 1

sample mean, xbar = 253
sample standard deviation, s = 11.4
sample size, n = 101
degrees of freedom, df = n - 1 = 100

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, tc = t(α/2, df) = 2.626

ME = tc * s/sqrt(n)
ME = 2.626 * 11.4/sqrt(101)
ME = 2.979

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (253 - 2.626 * 11.4/sqrt(101) , 253 + 2.626 * 11.4/sqrt(101))
CI = (250.02 , 255.98)