The average house price in Canada in 2010 was $339,100, according to the Canadian Real Estate Association (CREA). Today, a consumer group randomly selected a sample of 54 house prices and found an average price of $418,200 with a standard deviation of $94,300. The group put out a press release saying: “House prices have gone up by over 20% compared with 2010.”

a) Have average house prices increased? State your hypotheses and calculate a P-value. State any assumptions you’re making and whether they’re likely to be true.

b) Calculate the 95% confidence interval for the house prices today, assuming the conditions are satisfied. Comment on the validity of your confidence interval.

c) Comment on the ethics of the consumer group’s statement.