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# handout 9 - Sampling and sampling distributions Chapter 7...

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1 Sampling and sampling distributions. Chapter 7. So far, we have looked at simple techniques to display and summarize data, and at probability as a measure of uncertainty. Sample Population Describe the sample data Compute measures of variability Parameters are numerical descriptive measures for populations (fixed, often unknown values) For instance: For the normal distribution: the parameters are location and shape , described by µ and σ . For the binomial distribution : n and p. Statistics are numerical valued functions of the sample observations. (sample mean , sample variance). • We use sample statistics to make inferences about the corresponding population parameters. Statistics vary from sample to sample and hence are random variables. Ò Take 100 samples from the middle class Americans and record the age. The average age of the population is μ. Population X 1 …X N Sample 1, 35 x 1 = Sample 2, 37 x 2 = Sample 3, 34 x 3 = Sample 4, 36 x 4 = •The probability distributions for statistics are called sampling distributions . •The sampling distribution-the distribution of the possible values of a statistic is the probability distribution derived from repeatedly extracting samples of size n from the population. •The sampling distribution depends on a population distribution, sample size n, the way you choose your sample Sampling variability • Suppose I repeat the sampling 100 times. I will get different mean values. Values on the x-axes are the means computed in the 100 samples.

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2 N x μ i = where: N = Population size , n = sample size Sample Statistics are used to estimate population parameters Problems: Different samples provide different estimates of the population parameter Sample results have potential variability, thus sampling error exits.
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handout 9 - Sampling and sampling distributions Chapter 7...

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