A consumer interest group is concerned about rising prices for home in the Toronto real estate market. A random sample of 100 recently sold homes in Toronto yielded an average selling price of $428,900. Assume that the population standard deviation of the selling price of a home in Toronto is $67,500. At the 5% level of significance, is there enough evidence to indicate that the average selling price of all homes in Toronto exceeds $400,000? Under what conditions is this result valid?