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6-2 RANDOM SAMPLING 195

6-6. The following data are direct solar intensity measure- 35.80, 26.53, 64.63, 9.00, 15.38, 8.14, and 8.24. Prepare a
2
ments (watts/m ) on different days at a location in southern dot diagram for this second sample and compare it to the
Spain: 562, 869, 708, 775, 775, 704, 809, 856, 655, 806, one for the first sample. What can you conclude about
878, 909, 918, 558, 768, 870, 918, 940, 946, 661, 820, 898, CRT resolution in this situation?
935, 952, 957, 693, 835, 905, 939, 955, 960, 498, 653, 730, 6-11. The pH of a solution is measured eight times by one
and 753. Calculate the sample mean and sample standard operator using the same instrument. She obtains the following
deviation. data: 7.15, 7.20, 7.18, 7.19, 7.21, 7.20, 7.16, and 7.18.
6-7. The April 22, 1991 issue of Aviation Week and Space (a) Calculate the sample mean.
Technology reports that during Operation Desert Storm, U.S. (b) Calculate the sample variance and sample standard
Air Force F-117A pilots flew 1270 combat sorties for a total of deviation.
6905 hours. What is the mean duration of an F-117A mission (c) What are the major sources of variability in this experiment?
during this operation? Why is the parameter you have calcu- 6-12. An article in the Journal of Aircraft (1988) describes
lated a population mean? the computation of drag coefficients for the NASA 0012 air-
6-8. Preventing fatigue crack propagation in aircraft struc- foil. Different computational algorithms were used at
tures is an important element of aircraft safety. An engineering M
0.7 with the following results (drag coefficients are in
study to investigate fatigue crack in n 9 cyclically loaded units of drag counts; that is, one count is equivalent to a drag
wing boxes reported the following crack lengths (in mm): coefficient of 0.0001): 79, 100, 74, 83, 81, 85, 82, 80, and 84.
2.13, 2.96, 3.02, 1.82, 1.15, 1.37, 2.04, 2.47, 2.60. Compute the sample mean, sample variance, and sample stan-
(a) Calculate the sample mean. dard deviation, and construct a dot diagram.
(b) Calculate the sample variance and sample standard 6-13. The following data are the joint temperatures of the
deviation. O-rings (°F) for each test firing or actual launch of the space
(c) Prepare a dot diagram of the data. shuttle rocket motor (from Presidential Commission on the
6-9. Consider the solar intensity data in Exercise 6-6. Space Shuttle Challenger Accident, Vol. 1, pp. 129–131):
Prepare a dot diagram of this data. Indicate where the sample 84, 49, 61, 40, 83, 67, 45, 66, 70, 69, 80, 58, 68, 60, 67, 72,
mean falls on this diagram. Give a practical interpretation of 73, 70, 57, 63, 70, 78, 52, 67, 53, 67, 75, 61, 70, 81, 76, 79,
the sample mean. 75, 76, 58, 31.
6-10. Exercise 6-5 describes data from an article in Human (a) Compute the sample mean and sample standard deviation.
Factors on visual accommodation from an experiment involv- (b) Construct a dot diagram of the temperature data.
ing a high-resolution CRT screen. (c) Set aside the smallest observation 131 F2 and recompute
(a) Construct a dot diagram of this data. the quantities in part (a). Comment on your findings.
(b) Data from a second experiment using a low-resolution How “different” are the other temperatures from this
screen were also reported in the article. They are 8.85, last value?

6-2 RANDOM SAMPLING

In 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.

Definition
A population consists of the totality of the observations with which we are concerned.

In any particular problem, the population may be small, large but finite, or infinite. The
number of observations in the population is called the size of 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 distribution as a model for a popula-
tion. For example, a structural engineer might consider the population of tensile strengths of a