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274 CHAPTER 8 STATISTICAL INTERVALS FOR A SINGLE SAMPLE

0.6351 0.6275 0.6261 0.6262 0.6262 0.6314 (c) Find a 99% prediction interval on the tar content for the
0.6128 0.6403 0.6521 0.6049 0.6170 next observation that will be taken on this particular type
of tobacco.
0.6134 0.6310 0.6065 0.6214 0.6141
(d) Find an interval that will contain 99% of the values of the
tar content with 95% confidence.
(a) Is there evidence to support the assumption that the coef- (e) Explain the difference in the three intervals computed in
ficient of restitution is normally distributed? parts (b), (c), and (d).
(b) Find a 99% CI on the mean coefficient of restitution. 8-83. A manufacturer of electronic calculators takes a
(c) Find a 99% prediction interval on the coefficient of resti- random sample of 1200 calculators and finds that there are
tution for the next baseball that will be tested. eight defective units.
(d) Find an interval that will contain 99% of the values of the (a) Construct a 95% confidence interval on the population
coefficient of restitution with 95% confidence. proportion.
(e) Explain the difference in the three intervals computed in (b) Is there evidence to support a claim that the fraction of
parts (b), (c), and (d). defective units produced is 1% or less?
8-80. Consider the baseball coefficient of restitution data in 8-84. An article in The Engineer (“Redesign for Suspect
Exercise 8-79. Suppose that any baseball that has a coefficient Wiring,” June 1990) reported the results of an investigation
of restitution that exceeds 0.635 is considered too lively. into wiring errors on commercial transport aircraft that may
Based on the available data, what proportion of the baseballs produce faulty information to the flight crew. Such a wiring
in the sampled population are too lively? Find a 95% lower error may have been responsible for the crash of a British
confidence bound on this proportion. Midland Airways aircraft in January 1989 by causing the pilot
8-81. An article in the ASCE Journal of Energy Engineering to shut down the wrong engine. Of 1600 randomly selected
(“Overview of Reservoir Release Improvements at 20 TVA aircraft, eight were found to have wiring errors that could
Dams,” Vol. 125, April 1999, pp. 1–17) presents data on display incorrect information to the flight crew.
dissolved oxygen concentrations in streams below 20 dams in (a) Find a 99% confidence interval on the proportion of air-
the Tennessee Valley Authority system. The observations are (in craft that have such wiring errors.
milligrams per liter): 5.0, 3.4, 3.9, 1.3, 0.2, 0.9, 2.7, 3.7, 3.8, 4.1, (b) Suppose we use the information in this example to
1.0, 1.0, 0.8, 0.4, 3.8, 4.5, 5.3, 6.1, 6.9, and 6.5. provide a preliminary estimate of p. How large a sample
(a) Is there evidence to support the assumption that the would be required to produce an estimate of p that we are
dissolved oxygen concentration is normally distributed? 99% confident differs from the true value by at most
(b) Find a 95% CI on the mean dissolved oxygen concentra- 0.008?
tion. (c) Suppose we did not have a preliminary estimate of p. How
(c) Find a 95% prediction interval on the dissolved oxygen large a sample would be required if we wanted to be at
concentration for the next stream in the system that will be least 99% confident that the sample proportion differs
tested. from the true proportion by at most 0.008 regardless of the
(d) Find an interval that will contain 95% of the values of the true value of p?
dissolved oxygen concentration with 99% confidence. (d) Comment on the usefulness of preliminary information in
(e) Explain the difference in the three intervals computed in computing the needed sample size.
parts (b), (c), and (d). 8-85. An article in Engineering Horizons (Spring 1990,
8-82. The tar content in 30 samples of cigar tobacco p. 26) reported that 117 of 484 new engineering graduates
follows: were planning to continue studying for an advanced degree.
Consider this as a random sample of the 1990 graduating
class.
1.542 1.585 1.532 1.466 1.499 1.611 (a) Find a 90% confidence interval on the proportion of such
1.622 1.466 1.546 1.494 1.548 1.626 graduates planning to continue their education.
1.440 1.608 1.520 1.478 1.542 1.511 (b) Find a 95% confidence interval on the proportion of such
graduates planning to continue their education.
1.459 1.533 1.532 1.523 1.397 1.487
(c) Compare your answers to parts (a) and (b) and explain
1.598 1.498 1.600 1.504 1.545 1.558
why they are the same or different.
(d) Could you use either of these confidence intervals to
(a) Is there evidence to support the assumption that the tar determine whether the proportion is actually 0.25?
content is normally distributed? Explain your answer. Hint: Use the normal approximation
(b) Find a 99% CI on the mean tar content. to the binomial.