Question

The length of time it takes a car salesperson to close a deal on a car sale is assumed
to be normally distributed. A random sample of 100 such times was selected which
yielded a mean of 3 hours and variance of 0.5 hour.
The 98 percent confidence interval for the mean length of time it takes a car salesperson to sell a car is

Answer 1

sample mean, xbar = 3
sample standard deviation, s = 0.7071
sample size, n = 100
degrees of freedom, df = n - 1 = 99

Given CI level is 98%, hence α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01, tc = t(α/2, df) = 2.365

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (3 - 2.365 * 0.7071/sqrt(100) , 3 + 2.365 * 0.7071/sqrt(100))
CI = (2.83 , 3.17)