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Unformatted text preview: Sampling distributions for sample means IPS chapter 5.2 © 2006 W.H. Freeman and Company Objectives (IPS chapter 5.2) Sampling distribution of a sample mean Sampling distribution of x bar For normally distributed populations The central limit theorem. Reminder: What is a sampling distribution? The sampling distribution of a statistic is the distribution of all possible values taken by the statistic when all possible samples of a fixed size n are taken from the population. It is a theoretical idea — we do not actually build it. The sampling distribution of a statistic is the probability distribution of that statistic. The population distribution of a variable is the distribution of its values for all members of the population. The population distribution is also the probability distribution (sampling distribution ) of the variable when we choose one individual at random from the population. Example The distribution of heights of young women follows N(64.5, 2.5). Here 64.5 is the population mean , 2.5 is the population standard deviation. Select one young woman at random and measure her height (random variable X). In repeated sampling X will have the same N(64.5, 2.5) distribution. Sampling distribution of Sample Mean Now suppose that we take a random sample of 10 females, and calculate the mean height of this sample. Let’s denote this mean by ( x bar) .This is the sample mean ....
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 Fall '08
 ABDUS,S.
 Standard Deviation, W.H. Freeman

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