A random sample of 64 recently sold homes in Ottawa yielded an average selling price of $405,600. Assume that the population standard deviation of the selling price of a home in Ottawa is $67,500.
(a) Compute and interpret a 95% confidence interval for the population mean selling price of homes in Ottawa. Comment on the validity of this result.
(b) Suppose you wish to estimate the mean selling price of all homes in Ottawa to within $10,000 with 95% confidence. How many houses should be sampled in order to achieve the desired margin of error?
(c) Suppose we instead wished to use a 99% confidence level. Without doing any computations, how would this affect your answers in parts (a) and (b)?