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Error Bounds
Let
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Notes:
- If the error distribution is symmetric about zero, we can obtain the error bounds by solving for b in
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and then setting b1 = -b and b2 = b. In this case, b may also be interpreted as a bound for the error magnitude. Thus, if b is a 95% bound, then we have the assurance that the estimator is within b of the parameter (or estimand) with probability 0.95.- When the error distribution is normal with zero mean, the error bounds are
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and ![]()
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- As an example, suppose the sample mean is used as an estimator of the population mean. When based on a random sample from a normal distribution, error bounds for this point estimator are
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since in this case
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In practice, the population standard deviation is usually unknown and so we use
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as estimated error bounds for the sample mean where S is the usual sample standard deviation.- Similar error bounds may also be easily obtained for the usual estimators of a population proportion, difference of two means, difference of two proportions. Essentially, all you need to do is determine the standard errors of the relevant estimators.
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