274 CHAPTER 8 STATISTICAL INTERVALS FOR A SINGLE SAMPLE(c) Find a 99% prediction interval on the tar content for the
next observation that will be taken on this particular type
of tobacco.
(d) Find an interval that will contain 99% of the values of the
tar content with 95% confidence.
(e) Explain the difference in the three intervals computed in
parts (b), (c), and (d).
8-83. A manufacturer of electronic calculators takes a
random sample of 1200 calculators and finds that there are
eight defective units.
(a) Construct a 95% confidence interval on the population
proportion.
(b) Is there evidence to support a claim that the fraction of
defective units produced is 1% or less?
8-84. An article in The Engineer(“Redesign for Suspect
Wiring,” June 1990) reported the results of an investigation
into wiring errors on commercial transport aircraft that may
produce faulty information to the flight crew. Such a wiring
error may have been responsible for the crash of a British
Midland Airways aircraft in January 1989 by causing the pilot
to shut down the wrong engine. Of 1600 randomly selected
aircraft, eight were found to have wiring errors that could
display incorrect information to the flight crew.
(a) Find a 99% confidence interval on the proportion of air-
craft that have such wiring errors.
(b) Suppose we use the information in this example to
provide a preliminary estimate of p. How large a sample
would be required to produce an estimate of pthat we are
99% confident differs from the true value by at most
0.008?
(c) Suppose we did not have a preliminary estimate of p. How
large a sample would be required if we wanted to be at
least 99% confident that the sample proportion differs
from the true proportion by at most 0.008 regardless of the
true value of p?
(d) Comment on the usefulness of preliminary information in
computing the needed sample size.
8-85. An article in Engineering Horizons(Spring 1990,
p. 26) reported that 117 of 484 new engineering graduates
were planning to continue studying for an advanced degree.
Consider this as a random sample of the 1990 graduating
class.
(a) Find a 90% confidence interval on the proportion of such
graduates planning to continue their education.
(b) Find a 95% confidence interval on the proportion of such
graduates planning to continue their education.
(c) Compare your answers to parts (a) and (b) and explain
why they are the same or different.
(d) Could you use either of these confidence intervals to
determine whether the proportion is actually 0.25?
Explain your answer. Hint:Use the normal approximation
to the binomial.(a) Is there evidence to support the assumption that the coef-
ficient of restitution is normally distributed?
(b) Find a 99% CI on the mean coefficient of restitution.
(c) Find a 99% prediction interval on the coefficient of resti-
tution for the next baseball that will be tested.
(d) Find an interval that will contain 99% of the values of the
coefficient of restitution with 95% confidence.
(e) Explain the difference in the three intervals computed in
parts (b), (c), and (d).
8-80. Consider the baseball coefficient of restitution data in
Exercise 8-79. Suppose that any baseball that has a coefficient
of restitution that exceeds 0.635 is considered too lively.
Based on the available data, what proportion of the baseballs
in the sampled population are too lively? Find a 95% lower
confidence bound on this proportion.
8-81. An article in the ASCE Journal of Energy Engineering
(“Overview of Reservoir Release Improvements at 20 TVA
Dams,” Vol. 125, April 1999, pp. 1–17) presents data on
dissolved oxygen concentrations in streams below 20 dams in
the Tennessee Valley Authority system. The observations are (in
milligrams per liter): 5.0, 3.4, 3.9, 1.3, 0.2, 0.9, 2.7, 3.7, 3.8, 4.1,
1.0, 1.0, 0.8, 0.4, 3.8, 4.5, 5.3, 6.1, 6.9, and 6.5.
(a) Is there evidence to support the assumption that the
dissolved oxygen concentration is normally distributed?
(b) Find a 95% CI on the mean dissolved oxygen concentra-
tion.
(c) Find a 95% prediction interval on the dissolved oxygen
concentration for the next stream in the system that will be
tested.
(d) Find an interval that will contain 95% of the values of the
dissolved oxygen concentration with 99% confidence.
(e) Explain the difference in the three intervals computed in
parts (b), (c), and (d).
8-82. The tar content in 30 samples of cigar tobacco
follows:(a) Is there evidence to support the assumption that the tar
content is normally distributed?
(b) Find a 99% CI on the mean tar content.1.542
1.622
1.440
1.459
1.5981.585
1.466
1.608
1.533
1.4981.532
1.546
1.520
1.532
1.6001.466
1.494
1.478
1.523
1.5041.499
1.548
1.542
1.397
1.5451.611
1.626
1.511
1.487
1.5580.6351
0.6128
0.61340.6275
0.6403
0.63100.6261
0.6521
0.60650.6262
0.6049
0.62140.6262
0.6170
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