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6-6. The following data are direct solar intensity measurements (watts/m2) 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 Technology reports that during Operation Desert Storm, U.S. Air Force F-117A pilots ew 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 calculated a population mean 6-8. Preventing fatigue crack propagation in aircraft structures is an important element of aircraft safety. An engineering study to investigate fatigue crack in n 9 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 Factors on visual accommodation from an experiment involving 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,
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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 rst 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 coef cients for the NASA 0012 airfoil. Different computational algorithms were used at M 0.7 with the following results (drag coef cients are in units of drag counts; that is, one count is equivalent to a drag coef cient of 0.0001): 79, 100, 74, 83, 81, 85, 82, 80, and 84. Compute the sample mean, sample variance, and sample standard deviation, and construct a dot diagram. 6-13. The following data are the joint temperatures of the O-rings ( F) for each test ring 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 131 F2 and recompute the quantities in part (a). Comment on your findings. How different are the other temperatures from this last value
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In most statistics problems, we work with a sample of observations selected from the population that we are interested in studying. Figure 6-3 illustrates the relationship between the population and the sample. We have informally discussed these concepts before; however, we now give the formal de nitions of some of these terms. De nition A population consists of the totality of the observations with which we are concerned.
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In any particular problem, the population may be small, large but nite, or in nite. The number of observations in the population is called the size of the population. For example, the number of under lled bottles produced on one day by a soft-drink company is a population of nite size. The observations obtained by measuring the carbon monoxide level every day is a population of in nite size. We often use a probability distribution as a model for a population. For example, a structural engineer might consider the population of tensile strengths of a
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