285%2Bchap04-P3a

285%2Bchap04-P3a - Statistics Chapter 4 Random Variables...

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Chap 7-1 Statistics Chapter 4 Random Variables and Probability Distributions – Sampling Distributions Sections 4.10-4.11
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Chap 7-2 Chapter Goals After completing this chapter, you should be able to: Define the concept of sampling error Determine the mean and standard deviation for the sampling distribution of the sample mean, x Determine the mean and standard deviation for the sampling distribution of the sample proportion, p Describe the Central Limit Theorem and its importance Apply sampling distributions for both x and p _ _ _ _
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Chap 7-3 Sampling Error Sample Statistics are used to estimate Population Parameters ex: X is an estimate of the population mean, μ Problems: Different samples provide different estimates of the population parameter Sample results have potential variability, thus sampling error exits
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Chap 7-4 Calculating Sampling Error Sampling Error: The difference between a value (a statistic) computed from a sample and the corresponding value (a parameter) computed from a population Example: (for the mean) where: μ - x Error Sampling = mean population μ mean sample x = =
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Chap 7-5 Review Population mean: Sample Mean: N x μ i = where: μ = Population mean x = sample mean x i = Values in the population or sample N = Population size n = sample size n x x i =
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Chap 7-6 Example If the population mean is μ = 98.6 degrees and a sample of n = 5 temperatures yields a sample mean of = 99.2 degrees, then the sampling error is degrees 0.6 98.6 99.2 μ x = - = - x
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Chap 7-7 Sampling Errors Different samples will yield different sampling errors. The sampling error may be positive or negative ( may be greater than or less than μ). The expected sampling error decreases as the
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285%2Bchap04-P3a - Statistics Chapter 4 Random Variables...

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