A large city newspaper contains several hundred advertisements for one-bedroom apartments. You choose 25 at random and calculate a mean monthly rent of $703 and a standard deviation of $115.
(a) Explain why the sample mean is a random variable.
(b) What is the standard error of the sample mean? (Report a number)
(c) What are the degrees of freedom for a t statistic in this context?
(d) Construct a 95% confidence interval for the mean monthly rent of all advertised one-bedroom apartments.
(e) If you chose 90%, rather than 95%, confidence in the previous exercise, is it more or less likely that the interval contains the true mean? Explain.