Most people that travel to Quebec feels that gas prices there tend to be more than in Ontario. Suppose a random sample of 40 gas stations in Ontario in 2010 had an average price of $1.10/litre and a sample of 35 in Quebec was $1.15. Assume the population standard deviation is 0.08 in Ontario and 0.12 in Quebec. Let Ontario be population 1.
(a) Determine if there is a difference in gas prices between Ontario and Quebec. Use a test significance level of 0.01 and p-value approach. Clearly state hypothesis to be tested and conclusions.
(b) Suppose you were writing an article for the Toronto Star about the difference in mean gas prices and at the end of the article you make this statement: "The poll's margin of error for the difference in mean gas price is X, 18 times out of 20" What is the value of x?