Question

Assume that a sample is used to estimate a population mean μ . Find the 90% confidence interval for a sample of size 315 with a mean of 24.4 and a standard deviation of 18.8. Enter your answers accurate to one decimal place (because the sample statistics are reported accurate to one decimal place). (Fill both answers in the blank)

______ < μ < ______

Answer 1

sample mean, xbar = 24.4
sample standard deviation, s = 18.8
sample size, n = 315
degrees of freedom, df = n - 1 = 314

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 1.65

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (24.4 - 1.65 * 18.8/sqrt(315) , 24.4 + 1.65 * 18.8/sqrt(315))
CI = (22.7 , 26.1)