La Quinta Motor Inns developed a computer model to predict the profitability of sites that are beingconsidered as locations for new hotels. If the computer model predicts large profits, La Quinta buys theproposed site and builds a new hotel. If the computer model predicts small or moderate profits, La Quintachooses not to proceed. 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 aprofitable location.a. Explain the risks associated with committing a Type I error in this case.b. Explain the risks associated with committing a Type II error in this case.c. Which type of error do you think the executives at La Quinta Motor Inns are trying hard to avoid? Explain
Answers
Monroe College
STATISTICS
STATISTICS MG620
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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.
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?
Answer:
a) La Quinta Motor Inns commits a Type I error when it purchases a site that is not profitable.
(b) Type II error occurs when La Quinta Motor Inns fails to purchase a profitable site.
The cost to the Inns when a Type II error is committed is the loss on the amount of
profit the site could have generated had the Inns decided to purchase the site.
(c) The executives at La Quinta Motor Inns are trying to avoid a Type I error by
adopting a very stringent decision criterion. Only sites that are classified as
capable of generating high profit will be purchased.
Step-by-step explanation:
a) La Quinta Motor Inns commits a Type I error when it purchases a site that is not profitable.
(b) Type II error occurs when La Quinta Motor Inns fails to purchase a profitable site.
The cost to the Inns when a Type II error is committed is the loss on the amount of
profit the site could have generated had the Inns decided to purchase the site.
(c) The executives at La Quinta Motor Inns are trying to avoid a Type I error by
adopting a very stringent decision criterion. Only sites that are classified as
capable of generating high profit will be purchased.