Question

# 7) The Carpet Corner in Gladstone, Missouri, offers a variety of carpets, wood flooring, and tiles....

7) 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 1,250 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 = 1,305 square

feet. Assume that

σ = 155 square

feet.

a) Conduct a one-sided, right-tailed test of H0: μ = 1,250 versus Ha: μ > 1,250. Is there any evidence to suggest the true mean square footage is larger during a sale? Use α = 0.01. Calculate the test statistic. (Round your answer to four decimal places.)

z =

b) Find the probability of a Type II error if the true mean square footage during a sale is μa = 1,325; that is, find β(1,325). (Round your answer to four decimal places.)

β(1,325) =

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