The Federal Trade Commission (FTC) periodically conducts statistical studies designed to test the claims that manufacturers make about their products. For example, a label on the large can of Hilltop Coffee states that the can contains 3 pounds of coffee. The FTC knows that Hilltop's production process cannot place exactly 3 pounds of coffee in each can, even if the mean filling weight is at least 3 pounds per can. However, as long as the population mean filling weight is at least 3 pounds per can, the rights of consumers will be protected.
1. Formulate the null and alternate hypotheses for testing whether the mean filling weight per can of the sample is significantly less than that of the population.
2. Suppose a sample of 16 cans is chosen and the mean filling weight comes out to be 2.92 pounds. If the population standard deviation is 0.18, test whether the sample mean is significantly less than the population mean. Use .05 level of significance.