Pooled sample estimate
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Pooled estimator of the population proportion
A proportion is a ratio. Given a population divided into "successes" and "failures" the proportion of successes is the ratio of the number of successes to the total number of items in the population. The proportion may be sampled. The sample proportion is the ratio of the number of successes in the sample to the total number of trials. Given a single sample, we take the sample proportion, [Equation goes here &- download the original to see it.], as an estimate for the population proportion, [Equation goes here &- download the original to see it.]. For example, suppose that in a survey of 1200 housewives from a town in Kent 497 said they were in favour of a new by&-pass. Then the sample proportion would be [Equation goes here &- download the original to see it.] which would also be an estimate of the population proportion. When two sample proportions have been obtained, it makes sense to estimate the population proportion using both of them. In this case [Equation goes here &- download the original to see it.] gives an unbiased estimator of the population proportion, where [Equation goes here &- download the original to see it.] are the sample proportions.
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Contents of
Pooled sample estimate
1 Pooled sample estimate &- Population and sample
2 Pooling samples
3 Example of pooled sample estimate
4 Pooled estimator of the population proportion
5 Second Example of pooled sample estimate
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