Question

A study of the ages of motorcyclists killed in crashes involves the random selection of 143 drivers with a mean of 38.01 years. Assuming that sigmaequals8.8 ​years, construct and interpret a 99​% confidence interval estimate of the mean age of all motorcyclists killed in crashes.What is the 99​% confidence interval for the population mean u​?

Answer 1

sample mean, xbar = 38.01
sample standard deviation, σ = 8.8
sample size, n = 143

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, Zc = Z(α/2) = 2.5758

ME = zc * σ/sqrt(n)
ME = 2.5758 * 8.8/sqrt(143)
ME = 1.9

CI = (xbar - Zc * s/sqrt(n) , xbar + Zc * s/sqrt(n))
CI = (38.01 - 2.5758 * 8.8/sqrt(143) , 38.01 + 2.5758 * 8.8/sqrt(143))
CI = (36.1145 , 39.9055)
Therefore, based on the data provided, the 99% confidence interval for the population mean is 36.1145 < μ < 39.9055 which indicates that we are 99% confident that the true population mean μ is contained by the interval (36.1145 , 39.9055)

we are 99% confident taht the population mean is between 36.1145 and 39.9055