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Unformatted text preview: Chapter 8 – Sampling Distributions Defn : Sampling error is the error resulting from using a sample to infer a population characteristic. Example : We want to estimate the mean amount of Pepsi-Cola in 12-oz. cans coming off an assembly line by choosing a random sample of 16 cans, and using the sample mean as an estimate of the mean for the population of cans. Suppose that we choose 100 random samples of size 16 and compute the sample mean for each of these samples. These 100 values of X will differ from each other somewhat due to sampling error, but the values should all be close to 12- oz. Defn : For a random variable X, and a given sample size n, the distribution of the variable X , i.e., of all possible values of X , is called the sampling distribution of the mean . This probability distribution is a set of pairs of numbers. In each pair, the first number is a possible value of the sample mean, and the second number is the probability of obtaining that value of the mean occur when we select a random sample from the population. Properties of the Sampling Distribution of the Mean: 1) For samples of size n, the expectation (mean) of X , equals the expectation (mean) of X. In other words, X X μ μ = . 2) The possible values of X cluster closer around the population mean for larger samples than for smaller samples. In other words, the larger the sample size, the smaller the sampling error. In particular, the standard deviation of the sampling distribution of the means, X σ , will be smaller than the population standard deviation, X σ . In particular, we have n X X σ σ = , where n...
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This note was uploaded on 07/28/2011 for the course STA 2014 taught by Professor Staff during the Fall '10 term at University of Florida.
- Fall '10