Assume that the one-way commute time of an University of Colorado student from his house to school is a normally distributed random variable which we will call X. Furthermore, assume that the population standard deviation of X is σ = 10 minutes. Let μ be the unknown population mean for X.
(a) Experimental design: Determine a minimum sample size such that we will be 95 % confident that the error will not exceed 5 minutes when the sample average x ¯ is used to estimate μ. Let n denote this sample size.
(b) Randomly ask n people on the University of Colorado campus their commute times and record their answers.
(c) Based on your sample, find a 95% confidence interval using the central limit theorem (z-distribution).
(d) Now assume that we don't know the population standard deviation σ, use the t- distribution and the sample standard deviation S to find a 95% confidence interval.
(e) Test the null hypothesis that the mean commute time is 20 minutes at the significance level α = 0.01. You may assume that σ = 10 minutes.