6.75 The U.S. National Highway Traffic Safety Administration gathers data
concerning the causes of highway crashes where at least one fatality has occurred.
The following probabilities were determined from the 1998 annual study (BAC is
blood-alcohol content).
Source: Statistical Abstract of the United States, 2000, Table 1042.

P(BAC = 0 0 Crash with fatality) = .616
P(BAC is between .01 and .09 0 Crash with fatality) = .300
P(BAC is greater than .09 0 Crash with fatality) = .084
Over a certain stretch of highway during a 1-year period, suppose the probability
of being involved in a crash that results in at least one fatality is .01. It has been
estimated that 12% of the drivers on this highway drive while their BAC is greater
than .09. Determine the probability of a crash with at least one fatality if a driver
drives while legally intoxicated (BAC greater than .09).

6.81 Your favorite team team is in the final playoffs. You have assigned a
probability of 60% that it will win the championship. Past records indicate that
when teams win the championship, they win the first game of the series 70% of
the time. When they lose the series, they win the first game 25% of the time. The
first game is over; your team has lost. What is the probability that it will win the
series?
10.11 a. A random sample of 25 was drawn from a normal distribution with a
standard deviation of 5. The sample mean is 80. Determine the 95% confidence
interval 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 the
sample size increases.

11.52 A statistics practitioner wants to test the following hypotheses with = 20
and n = 100:
H0: = 100
H1: > 100
a. 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 a

11.60 Suppose that in Example 11.1 we wanted to determine whether there was
sufficient evidence to conclude that the new system would not be costeffective.
Set up the null and alternative hypotheses and discuss the consequences of Type I
and Type II errors. Conduct the test. Is your conclusion the same as the one
reached in Example 11.1? Explain.

EXAMPLE 11.1

Department Stores New Billing

System

The manager of a department store is thinking about establishing a new billing
system for the stores credit customers. After a thorough financial analysis, she
determines that the new system will be cost-effective only if the mean monthly
account is more than $170. A random sample of 400 monthly accounts is drawn, for
which the sample mean is $178. The manager knows that the accounts are
approximately normally distributed with a standard deviation of $65. Can the
manager conclude from this that the new system will be cost-effective?
SOLUTION:
IDENTIFY
This example deals with the population of the credit accounts at the store. To
conclude that the system will be cost-effective requires the manager to show that
the mean account for all customers is greater than $170. Consequently, we set up
the 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 as

H0: 170 (Do not install new system)
However, as was discussed in Section 11-1, we will actually test = 170, which is
how we specify the null hypothesis:
H0: = 170
As we previously pointed out, the test statistic is the best estimator of the
parameter. In Chapter 10, we used the sample mean to estimate the population
mean. To conduct this test, we ask and answer the following question: Is a sample
mean of 178 sufficiently greater than 170 to allow us to confidently infer that the
population mean is greater than 170?
There are two approaches to answering this question. The first is called the
rejection region method. It can be used in conjunction with the computer, but it is
mandatory for those computing statistics manually. The second is the p-value
approach, which in general can be employed only in conjunction with a computer
and statistical software. We recommend, however, that users of statistical software
be familiar with both approaches.
12.73 Xr12-73 With gasoline prices increasing, drivers are more concerned with
their cars gasoline consumption. For the past 5 years a driver has tracked the gas
mileage of his car and found that the variance from fill-up to fill-up was 2 = 23
mpg2. Now that his car is 5 years old, he would like to know whether the
variability of gas mileage has changed. He recorded the gas mileage from his last
eight fill-ups; these are listed here. Conduct a test at a 10% significance level to
infer whether the variability has changed.
28
25
29
25
32
36
27
24
12.74 Xr12-74 During annual checkups physicians routinely send their patients
to medical laboratories to have various tests performed. One such test determines
the cholesterol level in patients blood. However, not all tests are conducted in the
same way. To acquire more information, a man was sent to 10 laboratories and

had his cholesterol level measured in each. The results are listed here. Estimate
with 95% confidence the variance of these measurements.
188
193
186
184
190
195
187
190
192
196
The following exercises require the use of a computer and software. The answers
may be calculated manually.