Statistic Terms & Central Limit Theorem

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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 ...