# 989 among the questions to be raised are what is the

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9.89 Among the questions to be raised are: What is the goal of the experiment or research? Can it be translated into a null and alternative hypothesis? Is the hypothesis test going to be two- tailed or one-tailed? Can a random sample be drawn from the underlying population of interest? What kinds of measurements will be obtained from the sample? Are the sampled outcomes of the random variable going to be numerical or categorical? At what significance level, or risk of committing a Type I error, should the hypothesis test be conducted? Is the intended sample size large enough to achieve the desired power of the test for the level of significance chosen? What statistical test procedure is to be used on the sampled data and why? What kind of conclusions and interpretations can be drawn from the results of the hypothesis test? 9.90 (a) 0 1 : .5 : .5 H p H p (b) The level of significance is the probability of committing a Type I error, which is the probability of concluding the proportion of customers who prefer product one over product two is not 50% when in fact 50% of customers prefer product one over product two. The risk associated with Type II error is the probability of not rejecting the claim that 50% of customers prefer product one over product two when in fact the proportion of customers who prefer product one over product two is not 50%. (c) If we reject the null hypothesis for a p -value of 0.22, there is a 22% probability that we may have concluded that the proportion of customers preferring product one is not 50% while in fact 50% of customers prefer product one. (d) The article suggests raising the level of significance because the consequences of concluding the proportion of customers who prefer product one over product two is not 50% when in fact 50% of customers prefer product one are not very severe in the study. (e) Before raising the level of significance of a test, one has to evaluate genuinely whether the cost of committing a Type I error is really not as bad as one would have thought. (f) If the p -value is actually .12, we will be more confident about rejecting the null hypothesis. If the p -value is .06, we will be even more confident that a Type I error is much less likely to have occurred. 9.91 (a) La Quinta Motor Inns commits a Type I error when it purchases a site that is not profitable. If a Type I error has been committed, its cost will be the amount of lost
Solutions to End-of-Section and Chapter Review Problems 187 profit the Inns could have earned by using the money to purchase another profitable site. (b) Type II error occurs when La Quinta Motor Inns fails to purchase a profitable site. The cost to La Quinta Motor Inns when a Type II error is committed is the lost on the potential 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. Sites classified as capable of generating moderate profit will have a much higher likelihood of not being profitable. (d)