# Chap 7 - Chapter 7 Sampling and Sampling Distributions...

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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. Specifically know the characteristics (the expected value, standard error, and form) of the sampling distribution of the sample mean ( x ) and the sampling distribution of the sample proportion ( p ). 5. Understand the central limit theorem and the important role it plays in identifying the form (or shape) of the sampling distribution. 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 estimator point estimator point estimate 7 - 1

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Chapter 7 Solutions: 1. a. AB, AC, AD, AE, BC, BD, BE, CD, CE, DE b. With 10 samples, each has a 1/10 probability. c. B and D because the two smallest random numbers are .0476 and .0957. 2. The 4 smallest random numbers are .0341, .0729, .0936, and .1449. So elements 2, 3, 5, and 10 are the simple random sample. 3. The simple random sample consists of New York, Detroit, Oakland, Boston, and Kansas City. 4. Step 1: Generate a random number using the RAND() function for each of the 10 companies. Step 2: Sort the list of companies with respect to the random numbers. The first 3 companies in the sorted list make up the simple random sample. 5. Use the data disk accompanying the book and the EAI file. Generate a random number using the RAND() function for each of the 2500 managers. Then sort the list of managers with respect to the random numbers. The first 50 managers are the sample. 6. a. Finite population. A frame could be constructed obtaining a list of licensed drivers from the New York state driver’s license bureau. b. Sampling from a process. The process is the production line producing boxes of cereal. c. Sampling from a process. The process is one of generating arrivals to the Golden Gate Bridge. d. Finite population. A frame could be constructed by obtaining a listing of students enrolled in the course from the professor. e. Sampling from a process. The process is one of generating orders for the mail-order firm. 7. a. x x n i = = = Σ / 54 6 9 b. s x x n i = - - Σ ( ) 2 1 Σ ( ) x x i - 2 = (-4) 2 + (-1) 2 + 1 2 (-2) 2 + 1 2 + 5 2 = 48 s = 48 6 1 31 - = . 8. a. p = 75/150 = .50 b. p = 55/150 = .3667 9. a. x x n i = = = Σ / 465 5 93 b. 7 - 2
Sampling and Sampling Distributions x i ( ) x x i - ( ) x x i - 2 94 +1 1 100 +7 49 85 -8 64 94 +1 1 92 -1 1 Totals 465 0 116 s x x n i = - - = = Σ ( ) .

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## This note was uploaded on 11/08/2011 for the course MAT/FIN 272 taught by Professor Burns during the Spring '11 term at Central Connecticut State University.

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Chap 7 - Chapter 7 Sampling and Sampling Distributions...

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