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Statistic Terms & Central Limit Theorem

Define (a) parameter, (b) estimator, (c) sampling error, and (d) sampling distribution.

Part B: State the main points of Central Limit Theorem for a mean and explain.

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RESPONSE:

Define (a) parameter, (b) estimator, (c) sampling error, and (d) sampling distribution.

(a) A parameter

A parameter is a numerical quantity measuring some aspect of a population of scores. For example, the mean is a measure of central tendency. Greek letters are used to designate parameters. Parameters are rarely known and are usually estimated by statistics computed in samples. For example, examples of a parameter (and to the right of each Greek symbol is the symbol for the associated statistic used to estimate it from a sample) are the mean (¦Ì, M); standard deviation (¦Ò s); proportion (¦Ð, p); and correlation (¦Ñ, r). (http://davidmlane.com/hyperstat/A12328.html)

(b) Estimator

In statistics, because population parameters are often unknown, they need to be estimated. An estimator is defined as a function of the observable sample data that is used to estimate an unknown population parameter. For instance, to estimate a parameter of interest (e.g., a population mean, a binomial proportion, a difference between two population means, or a ratio of two population standard deviations), the usual procedure is as follows:

1. Select a random sample from the population of interest.
2. Calculate the point estimate of the parameter.
3. Calculate a measure of its variability, often a confidence interval.
4. Associate with this estimate a measure of variability.

Examples of ...

Solution Summary

This solution defines (a) parameter, (b) estimator, (c) sampling error, and (d) sampling distribution. It also states and explains the main points of Central Limit Theorem for a mean.

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