pp.114-131 fall 2009

# Pp.114-131 fall 2009 - 114 Random Sampling In general when we take a sample from a population we do it to estimate some characteristic(i.e

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Random Sampling In general, when we take a sample from a population we do it to estimate some characteristic (i.e. parameter) of a population with an appropriate statistic calculated from the sample. Of course, we want our sample to be representative of the population from which it was taken. In other words, we want our sample to be unbiased . If we want our sample to be unbiased and to be able to use our sample data to draw valid conclusions about our population, we need to employ random sampling . Simple random sampling is a method of sampling designed so that every item in the population has an equally likely chance of being selected. 114

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Sample Statistics and Sampling Distributions Very important concepts in statistics because they form the foundation for statistical inference . That is, they enable us to make valid statements about populations based on random samples drawn from those populations. Recall that a parameter is a characteristic of a population. For example, a population mean, µ, or a population standard deviation, σ. Usually, we do not know the true value of a parameter, but instead must estimate it by taking a random sample from the population and calculating a sample statistic from the sample data. The sample statistic serves as a point estimate for the population parameter. For example, x is a point estimate for µ and s is a point estimate for σ . Also, a point estimate for the binomial parameter, p, can be obtained by taking a random sample of size n from a population, calculating the number of items (or objects or people) that have the characteristic of interest. A point estimate of p can then be calculated as p = x/n. So, the sample statistic p is a point estimate of p. Sampling Distributions : Sample statistics are summary measures obtained from random samples. Sample statistics are themselves random variables. So, x, s, and p are random variables, just like x is a random variable. As such, x, s, and p have 115
probability distributions. A sampling distribution is simply a probability distribution for a statistic. They are important because they allow us to say how reliable the point estimate (sample statistic) is. For example, suppose that I find that the mean selling price for a sample of 50 homes in South Carolina was x=\$154,500 last month. I know that this value almost

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## This note was uploaded on 06/06/2011 for the course MGSC 291 taught by Professor Rollins during the Fall '09 term at South Carolina.

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Pp.114-131 fall 2009 - 114 Random Sampling In general when we take a sample from a population we do it to estimate some characteristic(i.e

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