Posted: May 22nd, 2023

Interval estimates for a sample mean can be contrasted from point estimates for the population mean, for example, the value could be given as a 95% confidence interval. A point estimate is a single figure that is given as an approximation of the for a population mean of some observation or statistical experiment. In contrast, an interval estimate specifies a range within which the approximated mean of the population lies. Both of these estimates are used to indicate the reliability of a population.

Since the estimate for the population mean is applicable to the whole population, it must have certain characteristics, i.e. it must be consistent within the whole population, it must be unbiased (must be centered on the actual population mean), and it must have a small standard error (the lower the error, the more reliable it is). For example, if we have a population sample (x_{1}, x_{2}â€¦ x_{n}), a point estimate for the mean, sayÂ *Î¸,*Â would be one that can be used in place of the individual observations. The estimator can be rejected if it cannot be used in place many observations (Groebner, 2007).

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Interval estimates for a sample mean can be contrasted from point estimates for the population mean

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An interval estimate gives more information about a population characteristic than a point estimate. Confidence intervals are sometimes referred to as confidence intervals. The general formula for computing the confidence value is

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