1. La Quinta Motor Inns developed a computer model to help predict the profitability of sites that are being considered as locations for new hotels. If the computer model predicts large profits, La Quinta buys the proposed site and builds a new hotel. If the computer model predicts small or moderate profits, La Quinta chooses not to proceed with that site (Extracted from S. E. Kimes and J. A. Fitzsimmons,Selecting Profitable Hotel Sites at La Quinta Motor Inns, Interfaces, Vol. 20, March April 1990, pp. 12 20).This decision-making procedure can be expressed in the hypothesis-testing framework. The null hypothesis is that the site is not a profitable location. The alternative hypothesis is that the site is a profitable location.
1a. Explain the risks associated with committing a Type I error in this case.
1b. Explain the risks associated with committing a Type II error in this case.
1c. Which type of error do you think the executives at La Quinta Motor Inns are trying hard to avoid? Explain.
1d. How do changes in the rejection criterion affect the probabilities of committing Type I and Type II errors?
2. The owner of a gasoline station wants to study gasoline purchasing habits by motorists at his station. He selects a random sample of 60 motorists during a certain week, with the following results:The average mount purchased was = 11.3 gallons, S = 3.1 gallons.11 motorists purchased premium-grade gasoline.
2a. At the 0.05 level of significance, is there evidence that the mean purchase was different from 10 gallons?
2b. Determine the p-value in (a).
2c. At the 0.05 level of significance, is there evidence that fewer than 20% of all the motorists at the station purchased premium-grade gasoline?
2d. What is your answer to (a) if the sample mean equals10.3 gallons?
2e. What is your answer to (c) if 7 motorists purchased premium-grade gasoline?