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handout7 - Notes Chapter 7 Sampling Distributions Bin Wang...

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Chapter 7: Sampling Distributions Bin Wang [email protected] Department of Mathematics and Statistics University of South Alabama Mann E6 1/24 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 E6 2/24 Mann E6 3/24 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 E6 4/24 Notes Notes Notes Notes
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Mann E6 5/24 Mann E6 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. Definition (Nonsampling Errors) The errors that occurs in the collection, recording, and tabulation of data are called nonsampling errors. Mann E6 7/24 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 Now suppose when we select the sample of three scores, we mistakenly record the second score as 82 instead of 80. ¯ x = 70 + 82 + 95 3 = 82 . 33 and ¯ x - μ = 82 . 33 - 80 . 60 = 1 . 73 The different 1.73 consists of the sampling error and nonsampling error.
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