6-2 RANDOM SAMPLINGIn most statistics problems, we work with a sample of observations selected from the popula-
tion that we are interested in studying. Figure 6-3 illustrates the relationship between the pop-
ulation and the sample. We have informally discussed these concepts before; however, we
now give the formal definitions of some of these terms.6-6. The following data are direct solar intensity measure-
ments (watts/m^2 ) on different days at a location in southern
Spain: 562, 869, 708, 775, 775, 704, 809, 856, 655, 806,
878, 909, 918, 558, 768, 870, 918, 940, 946, 661, 820, 898,
935, 952, 957, 693, 835, 905, 939, 955, 960, 498, 653, 730,
and 753. Calculate the sample mean and sample standard
deviation.
6-7. The April 22, 1991 issue of Aviation Week and Space
Technologyreports that during Operation Desert Storm, U.S.
Air Force F-117A pilots flew 1270 combat sorties for a total of
6905 hours. What is the mean duration of an F-117A mission
during this operation? Why is the parameter you have calcu-
lated a population mean?
6-8. Preventing fatigue crack propagation in aircraft struc-
tures is an important element of aircraft safety. An engineering
study to investigate fatigue crack in n9 cyclically loaded
wing boxes reported the following crack lengths (in mm):
2.13, 2.96, 3.02, 1.82, 1.15, 1.37, 2.04, 2.47, 2.60.
(a) Calculate the sample mean.
(b) Calculate the sample variance and sample standard
deviation.
(c) Prepare a dot diagram of the data.
6-9. Consider the solar intensity data in Exercise 6-6.
Prepare a dot diagram of this data. Indicate where the sample
mean falls on this diagram. Give a practical interpretation of
the sample mean.
6-10. Exercise 6-5 describes data from an article in Human
Factorson visual accommodation from an experiment involv-
ing a high-resolution CRT screen.
(a) Construct a dot diagram of this data.
(b) Data from a second experiment using a low-resolution
screen were also reported in the article. They are 8.85,35.80, 26.53, 64.63, 9.00, 15.38, 8.14, and 8.24. Prepare a
dot diagram for this second sample and compare it to the
one for the first sample. What can you conclude about
CRT resolution in this situation?
6-11. The pH of a solution is measured eight times by one
operator using the same instrument. She obtains the following
data: 7.15, 7.20, 7.18, 7.19, 7.21, 7.20, 7.16, and 7.18.
(a) Calculate the sample mean.
(b) Calculate the sample variance and sample standard
deviation.
(c) What are the major sources of variability in this experiment?
6-12. An article in the Journal of Aircraft(1988) describes
the computation of drag coefficients for the NASA 0012 air-
foil. Different computational algorithms were used at
with the following results (drag coefficients are in
units of drag counts; that is, one count is equivalent to a drag
coefficient of 0.0001): 79, 100, 74, 83, 81, 85, 82, 80, and 84.
Compute the sample mean, sample variance, and sample stan-
dard deviation, and construct a dot diagram.
6-13. The following data are the joint temperatures of the
O-rings (°F) for each test firing or actual launch of the space
shuttle rocket motor (from Presidential Commission on the
Space Shuttle Challenger Accident, Vol. 1, pp. 129–131):
84, 49, 61, 40, 83, 67, 45, 66, 70, 69, 80, 58, 68, 60, 67, 72,
73, 70, 57, 63, 70, 78, 52, 67, 53, 67, 75, 61, 70, 81, 76, 79,
75, 76, 58, 31.
(a) Compute the sample mean and sample standard deviation.
(b) Construct a dot diagram of the temperature data.
(c) Set aside the smallest observation and recompute
the quantities in part (a). Comment on your findings.
How “different” are the other temperatures from this
last value?131 F 2M 0.7A populationconsists of the totality of the observations with which we are concerned.DefinitionIn any particular problem, the population may be small, large but finite, or infinite. The
number of observations in the population is called the sizeof the population. For example, the
number of underfilled bottles produced on one day by a soft-drink company is a population of
finite size. The observations obtained by measuring the carbon monoxide level every day is a
population of infinite size. We often use a probability distributionas a modelfor a popula-
tion. For example, a structural engineer might consider the population of tensile strengths of a6-2 RANDOM SAMPLING 195c 06 .qxd 5/14/02 9:54 M Page 195 RK UL 6 RK UL 6:Desktop Folder:TEMP WORK:MONTGOMERY:REVISES UPLO D CH114 FIN L:Quark Files: