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Unformatted text preview: Chapter 7: Sampling Distributions Bin Wang [email protected] Department of Mathematics and Statistics University of South Alabama Mann E7 1/24 7.1 Population and Sampling Distributions Definition The population distribution is the probability distribution of the population data. Mann E7 2/24 7.1 Population and Sampling Distributions Definition The population distribution is the probability distribution of the population data. Example 70 78 80 80 95 Mann E7 2/24 7.1 Population and Sampling Distributions Definition The population distribution is the probability distribution of the population data. Example 70 78 80 80 95 Mann E7 2/24 Mann E7 3/24 7.1 Population and Sampling Distributions Definition The probability distribution of the sample mean ¯ x is called the sampling distribution of ¯ x . Mann E7 4/24 7.1 Population and Sampling Distributions Definition The probability distribution of the sample mean ¯ x is called the sampling distribution of ¯ x . In general, the porbability distribution of a sample statistic is called its sampling distribution. Mann E7 4/24 Mann E7 5/24 Mann E7 6/24 Mann E7 6/24 7.2 Sampling and Nonsampling Errors Definition (Sampling Error) Sampling error is the difference between the value of a sample statistic and the value of the corresponding population parameter. In the case of mean, sampling error = ¯ x μ assuming the sample is random and no nonsampling error has been made. Mann E7 7/24 7.2 Sampling and Nonsampling Errors Definition (Sampling Error) Sampling error is the difference between the value of a sample statistic and the value of the corresponding population parameter. In the case of mean, sampling error = ¯ x μ assuming the sample is random and no nonsampling error has been made. Definition (Nonsampling Errors) The errors that occurs in the collection, recording, and tabulation of data are called nonsampling errors. Mann E7 7/24 Example Population data: 70,78,80,80,95. Draw a sample: 70, 80, 95. Mann E7 8/24 Example Population data: 70,78,80,80,95. Draw a sample: 70, 80, 95. μ = 80 . 60 Mann E7 8/24 Example Population data: 70,78,80,80,95. Draw a sample: 70, 80, 95. μ = 80 . 60 and ¯ x = 70 + 80 + 95 3 = 81 . 67 Mann E7 8/24 Example Population data: 70,78,80,80,95. Draw a sample: 70, 80, 95. μ = 80 . 60 and ¯ x = 70 + 80 + 95 3 = 81 . 67 Sampling error = ¯ x μ = 81 . 67 80 . 60 = 1 . 07 Mann E7 8/24 Example Population data: 70,78,80,80,95....
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 Fall '09
 Wangs
 Normal Distribution, µ, Mann E7

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