Marketing and Consumer Behavior The Carpet Corner in Gladstone, Missouri, offers a variety of carpets, wood flooring, and tiles. Sales records indicate that the mean amount of carpet installed in a wall-to-wall carpeted residential home by crews from this store is 1250 square feet. The store manager, Frank Vida, believes that when there is a sale, customers translate the savings into carpeting a larger area. A random sample of 45 wall-to-wall carpet purchases was selected during a sale. The sample mean was x‾ = 1305 square feet; assume that σ = 155 square feet.
a. Conduct a one-sided, right-tailed test of H0: μ = 1250 versus Ha: μ > 1250. Is there any evidence to suggest the true mean square footage is larger during a sale? Use a = 0.01.
b. Find the probability of a type II error if the true mean square footage during a sale is μa = 1330; that is, find β(1330).
c. Carefully sketch a graph that includes the distribution of X if μ = 1250 and if μ = 1330. Shade in the areas that correspond to the probability of a type I error (0.01) and to the probability of a type II error found in part (b).