1. According to Road & Track Magazine, the average price for a four-door American-made sedan is $29,445 with a standard deviation of $5,400. A car shopper believes the average price may be different than that and samples 100 cars to test her theory. The sample result shows average price to be $30,700. Develop a critical value test that uses ninety-nine percent confidence to mathematically test this hypothesis. Is the shopper right?
2. In a recent survey, a company claimed that no more than 40% of all citizens believed the country was in a recession. In a random sample of 375 citizens, 175 stated they believed the country was in a recession. Use a .02 level of significance and test the company's claim based on the critical value.