Question;6.75 The U.S. National Highway Traffic Safety Administration gathers dataconcerning the causes of highway crashes where at least one fatality has occurred.The following probabilities were determined from the 1998 annual study (BAC isblood-alcohol content).Source: Statistical Abstract of the United States, 2000, Table 1042.P(BAC = 0 0 Crash with fatality) =.616P(BAC is between.01 and.09 0 Crash with fatality) =.300P(BAC is greater than.09 0 Crash with fatality) =.084Over a certain stretch of highway during a 1-year period, suppose the probabilityof being involved in a crash that results in at least one fatality is.01. It has beenestimated that 12% of the drivers on this highway drive while their BAC is greaterthan.09. Determine the probability of a crash with at least one fatality if a driverdrives while legally intoxicated (BAC greater than.09).6.81 Your favorite team team is in the final playoffs. You have assigned aprobability of 60% that it will win the championship. Past records indicate thatwhen teams win the championship, they win the first game of the series 70% ofthe time. When they lose the series, they win the first game 25% of the time. Thefirst game is over, your team has lost. What is the probability that it will win theseries?10.11 a. A random sample of 25 was drawn from a normal distribution with astandard deviation of 5. The sample mean is 80. Determine the 95% confidenceinterval estimate of the population mean.b. Repeat part (a) with a sample size of 100.c. Repeat part (a) with a sample size of 400.d. Describe what happens to the confidence interval estimate when thesample size increases.11.52 A statistics practitioner wants to test the following hypotheses with = 20and n = 100:H0: = 100H1: > 100a. Using a =.10 find the probability of a Type II error when = 102.b. Repeat part (a) with a =.02.c. Describe the effect on of decreasing a11.60 Suppose that in Example 11.1 we wanted to determine whether there wassufficient evidence to conclude that the new system would not be costeffective.Set up the null and alternative hypotheses and discuss the consequences of Type Iand Type II errors. Conduct the test. Is your conclusion the same as the onereached in Example 11.1? Explain.EXAMPLE 11.1Department Stores New BillingSystemThe manager of a department store is thinking about establishing a new billingsystem for the stores credit customers. After a thorough financial analysis, shedetermines that the new system will be cost-effective only if the mean monthlyaccount is more than $170. A random sample of 400 monthly accounts is drawn, forwhich the sample mean is $178. The manager knows that the accounts areapproximately normally distributed with a standard deviation of $65. Can themanager conclude from this that the new system will be cost-effective?SOLUTION:IDENTIFYThis example deals with the population of the credit accounts at the store. Toconclude that the system will be cost-effective requires the manager to show thatthe mean account for all customers is greater than $170. Consequently, we set upthe alternative hypothesis to express this circumstance:H1: > 170 (Install new system)If the mean is less than or equal to 170, then the system will not be cost-effective.The null hypothesis can be expressed asH0: 170 (Do not install new system)However, as was discussed in Section 11-1, we will actually test = 170, which ishow we specify the null hypothesis:H0: = 170As we previously pointed out, the test statistic is the best estimator of theparameter. In Chapter 10, we used the sample mean to estimate the populationmean. To conduct this test, we ask and answer the following question: Is a samplemean of 178 sufficiently greater than 170 to allow us to confidently infer that thepopulation mean is greater than 170?There are two approaches to answering this question. The first is called therejection region method. It can be used in conjunction with the computer, but it ismandatory for those computing statistics manually. The second is the p-valueapproach, which in general can be employed only in conjunction with a computerand statistical software. We recommend, however, that users of statistical softwarebe familiar with both approaches.12.73 Xr12-73 With gasoline prices increasing, drivers are more concerned withtheir cars gasoline consumption. For the past 5 years a driver has tracked the gasmileage of his car and found that the variance from fill-up to fill-up was 2 = 23mpg2. Now that his car is 5 years old, he would like to know whether thevariability of gas mileage has changed. He recorded the gas mileage from his lasteight fill-ups, these are listed here. Conduct a test at a 10% significance level toinfer whether the variability has changed.282529253236272412.74 Xr12-74 During annual checkups physicians routinely send their patientsto medical laboratories to have various tests performed. One such test determinesthe cholesterol level in patients blood. However, not all tests are conducted in thesame way. To acquire more information, a man was sent to 10 laboratories andhad his cholesterol level measured in each. The results are listed here. Estimatewith 95% confidence the variance of these measurements.188193186184190195187190192196The following exercises require the use of a computer and software. The answersmay be calculated manually.
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