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Sampling and Sampling Distributions

Sampling and Sampling Distributions. 2013/12/02. Sampling methods. Random sampling : Choose the elements for the sample one at a time in such a way that, at each step, each of the events remaining in the population has the same probability of being selected.

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Sampling and Sampling Distributions

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  1. Sampling and Sampling Distributions 2013/12/02

  2. Sampling methods • Random sampling: Choose the elements for the sample one at a time in such a way that, at each step, each of the events remaining in the population has the same probability of being selected. • Cluster sampling: The elements in the population are first divided into separate groups called clusters. Each elements of the population belongs to one and only one cluster. A simple random sample of the cluster is taken. • Systematic sampling: Select a simple random sample by first finding a random number and then counting or searching through the list of the population. • Convenience sampling: A nonprobability sampling technique.

  3. Population vs. Sample • A primary purpose of statistical inference is to develop estimates and test hypotheses about population parameters using information contained in a sample. • Population vs. sample • A population is the set of all the elements of interest in a study. • Numerical characteristics of a population are called parameters. • A sample is a subset of the population. • Numerical characteristics of a sample are called statistics.

  4. Point estimation • To estimate the value of a population parameter, we compute a corresponding sample statistic. • We refer to the sample mean , standard deviation s, and proportion as the point estimators of the population mean μ, standard deviation σ, and proportion prespectively. • Ex. P. 266 ex 13 & ex 15

  5. Sampling distribution • Suppose we repeat the process of selecting a sample random sample over and over again, each time computing the sample statistics. • The probability distribution of the sample statistic is called the sampling distribution of the statistic. • P. 272 Figure 7.3

  6. Central Limit Theorem • In selecting simple random samples of size n from a population, the sampling distribution of the sample mean can be approximated by a normal distribution as the sample size becomes large. • Central Limit Theorem: If n is large,

  7. Sampling size • Ex. P259 EAI example • Ex. P274 Question • As the sample size is increased, the standard deviation of the sampling distribution of decreases. • Ex. P276 Question

  8. Sampling distribution of • The sampling distribution of can be approximated by a normal distribution whenever np≥5 and n(1-p)≥5 • Expected value of is p. • Standard deviation of is • Ex. P282 Figure 7.8

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