Ch07 - Chapter 7 Sampling and Sampling Distributions...

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7 - 1 Chapter 7 Sampling and Sampling Distributions Learning Objectives 1. Understand the importance of sampling and how results from samples can be used to provide estimates of population characteristics such as the population mean, the population standard deviation and / or the population proportion. 2. Know what simple random sampling is and how simple random samples are selected. 3. Understand the concept of a sampling distribution. 4. Understand the central limit theorem and the important role it plays in sampling. 5. Specifically know the characteristics of the sampling distribution of the sample mean ( x ) and the sampling distribution of the sample proportion ( p ). 6. Learn about a variety of sampling methods including stratified random sampling, cluster sampling, systematic sampling, convenience sampling and judgment sampling. 7. Know the definition of the following terms: parameter sampling distribution sample statistic finite population correction factor simple random sampling standard error sampling without replacement central limit theorem sampling with replacement unbiased point estimator relative efficiency point estimate consistency
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Chapter 7 7 - 2 Solutions: 1. a. AB, AC, AD, AE, BC, BD, BE, CD, CE, DE b. With 10 samples, each has a 1/10 probability. c. E and C because 8 and 0 do not apply.; 5 identifies E; 7 does not apply; 5 is skipped since E is already in the sample; 3 identifies C; 2 is not needed since the sample of size 2 is complete. 2. Using the last 3-digits of each 5-digit grouping provides the random numbers: 601, 022, 448, 147, 229, 553, 147, 289, 209 Numbers greater than 350 do not apply and the 147 can only be used once. Thus, the simple random sample of four includes 22, 147, 229, and 289. 3. 459, 147, 385, 113, 340, 401, 215, 2, 33, 348 4. a. 6, 8, 5, 4, 1 Nasdaq 100, Oracle, Microsoft, Lucent, Applied Materials b. !1 0 ! 3 , 6 2 8 , 5 0 0 252 !( )! 5!(10 5)! (120)(120) N nN n == = −− 5. 283, 610, 39, 254, 568, 353, 602, 421, 638, 164 6. 2782, 493, 825, 1807, 289 7. 108, 290, 201, 292, 322, 9, 244, 249, 226, 125, (continuing at the top of column 9) 147, and 113. 8. 13, 8, 23, 25, 18, 5 The second occurrences of random numbers 13 and 25 are ignored. Maryland, Iowa, Florida State, Virginia, Pittsburgh, Oklahoma 9. 102, 115, 122, 290, 447, 351, 157, 498, 55, 165, 528, 25 10. finite, infinite, infinite, infinite, finite 11. a. xx n i = Σ / 54 6 9 b. s n i = Σ () 2 1 Σ i 2 = (-4) 2 + (-1) 2 + 1 2 (-2) 2 + 1 2 + 5 2 = 48 s = 48 61 31 = .
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Sampling and Sampling Distributions 7 - 3 12. a. p = 75/150 = .50 b. p = 55/150 = .3667 13. a. xx n i == = Σ / 465 5 93 b. x i () i i 2 94 +1 1 100 +7 49 85 -8 64 94 +1 1 92 -1 1 Totals 465 0 116 s n i = Σ .
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Ch07 - Chapter 7 Sampling and Sampling Distributions...

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