Page 324 - Applied statistics and probability for engineers

302 Chapter 8/Statistical intervals for a single sample

(b) An interval that contains 99% of the hemoglobin values (a) Is there evidence to support the assumption that the dis-
with 90% conidence. solved oxygen concentration is normally distributed?
8-102. Consider the compressive strength of concrete (b) Find a 95% CI on the mean dissolved oxygen concentration.
data from Exercise 8-99. Find a 95% prediction interval on the (c) Find a 95% prediction interval on the dissolved oxygen con-
next sample that will be tested. centration for the next stream in the system that will be tested.
8-103. The maker of a shampoo knows that customers like (d) Find an interval that will contain 95% of the values of the
this product to have a lot of foam. Ten sample bottles of the dissolved oxygen concentration with 99% conidence.
product are selected at random and the foam heights observed (e) Explain the difference in the three intervals computed in
are as follows (in millimeters): 210, 215, 194, 195, 211, 201, parts (b), (c), and (d).
198, 204, 208, and 196. 8-107. The tar content in 30 samples of cigar tobacco follows:
(a) Is there evidence to support the assumption that foam
height is normally distributed? 1.542 1.585 1.532 1.466 1.499 1.611
(b) Find a 95% CI on the mean foam height. 1.622 1.466 1.546 1.494 1.548 1.626
(c) Find a 95% prediction interval on the next bottle of sham- 1.440 1.608 1.520 1.478 1.542 1.511
poo that will be tested. 1.459 1.533 1.532 1.523 1.397 1.487
(d) Find an interval that contains 95% of the shampoo foam 1.598 1.498 1.600 1.504 1.545 1.558
heights with 99% conidence. (a) Is there evidence to support the assumption that the tar
(e) Explain the difference in the intervals computed in parts content is normally distributed?
(b), (c), and (d). (b) Find a 99% CI on the mean tar content.
8-104. During the 1999 and 2000 baseball seasons, there was (c) Find a 99% prediction interval on the tar content for the
much speculation that the unusually large number of home runs next observation that will be taken on this particular type
hit was due at least in part to a livelier ball. One way to test the of tobacco.
“liveliness” of a baseball is to launch the ball at a vertical surface (d) Find an interval that will contain 99% of the values of the
with a known velocity V and measure the ratio of the outgo- tar content with 95% conidence.
L
ing velocity V of the ball to V . The ratio R = V /V is called (e) Explain the difference in the three intervals computed in
O L O L
the coeficient of restitution. Following are measurements of the parts (b), (c), and (d).
coeficient of restitution for 40 randomly selected baseballs. The 8-108. A manufacturer of electronic calculators takes
balls were thrown from a pitching machine at an oak surface. a random sample of 1200 calculators and inds 8 defective
units.
0.6248 0.6237 0.6118 0.6159 0.6298 0.6192
0.6520 0.6368 0.6220 0.6151 0.6121 0.6548 (a) Construct a 95% conidence interval on the population
0.6226 0.6280 0.6096 0.6300 0.6107 0.6392 proportion.
0.6230 0.6131 0.6223 0.6297 0.6435 0.5978 (b) Is there evidence to support a claim that the fraction of
0.6351 0.6275 0.6261 0.6262 0.6262 0.6314 defective units produced is 1% or less?
0.6128 0.6403 0.6521 0.6049 0.6170 8-109. An article in The Engineer (“Redesign for Sus-
0.6134 0.6310 0.6065 0.6214 0.6141 pect Wiring,” June 1990) reported the results of an investiga-
(a) Is there evidence to support the assumption that the coef- tion into wiring errors on commercial transport aircraft that
icient of restitution is normally distributed? may display faulty information to the light crew. Such a wir-
(b) Find a 99% CI on the mean coeficient of restitution. ing error may have been responsible for the crash of a British
(c) Find a 99% prediction interval on the coeficient of restitu- Midland Airways aircraft in January 1989 by causing the pilot
tion for the next baseball that will be tested. to shut down the wrong engine. Of 1600 randomly selected
(d) Find an interval that will contain 99% of the values of the aircraft, 8 were found to have wiring errors that could display
coeficient of restitution with 95% conidence. incorrect information to the light crew.
(e) Explain the difference in the three intervals computed in (a) Find a 99% conidence interval on the proportion of aircraft
parts (b), (c), and (d). that have such wiring errors.
8-105. Consider the baseball coeficient of restitution (b) Suppose that you use the information in this example to
data in Exercise 8-104. Suppose that any baseball that has provide a preliminary estimate of p. How large a sample
a coeficient of restitution that exceeds 0.635 is considered would be required to produce an estimate of p that we are
too lively. Based on the available data, what proportion of 99% conident differs from the true value by at most 0.008?
the baseballs in the sampled population are too lively? Find a (c) Suppose that you did not have a preliminary estimate of p.
95% lower conidence bound on this proportion. How large a sample would be required if you wanted to be at
8-106 An article in the ASCE Journal of Energy Engi- least 99% conident that the sample proportion differs from
neering [“Overview of Reservoir Release Improvements at 20 the true proportion by at most 0.008 regardless of the true
TVA Dams” (Vol. 125, April 1999, pp. 1–17)] presents data on value of p?
dissolved oxygen concentrations in streams below 20 dams in (d) Comment on the usefulness of preliminary information in
the Tennessee Valley Authority system. The observations are computing the needed sample size.
(in milligrams per liter): 5.0, 3.4, 3.9, 1.3, 0.2, 0.9, 2.7, 3.7, 8-110. An article in Engineering Horizons (Spring 1990,
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. p. 26) reported that 117 of 484 new engineering graduates were