Contents
What does efficiency of an estimator mean?
For an unbiased estimator, efficiency indicates how much its precision is lower than the theoretical limit of precision provided by the Cramer-Rao inequality. A measure of efficiency is the ratio of the theoretically minimal variance to the actual variance of the estimator.
Which estimator is most efficient?
Efficiency: The most efficient estimator among a group of unbiased estimators is the one with the smallest variance. For example, both the sample mean and the sample median are unbiased estimators of the mean of a normally distributed variable. However, X has the smallest variance.
Why is there an error in estimating the population mean?
The error is due to random chance. Likewise, a sample mean is an estimate for the population mean, but there will be some error due to random chance. Recall that, in Inference for One Proportion, we adjusted the standard error by replacing p with the sample proportion.
How to calculate the confidence interval of a population mean?
The general format of a confidence interval estimate of a population mean is: For variable X j, a confidence interval estimate of its population mean μ j is In this formula, x ¯ j is the sample mean, s j is the sample standard deviation and n is the sample size.
What is the point estimate of the population proportion?
A point estimate of the population proportion is given by the sample proportion. With knowledge of the sampling distribution of the sample proportion, an interval estimate of a population proportion is obtained in much the same fashion as for a population mean.
Which is the weak point in estimating the population?
The weak point is the estimate of the population variance used. We do not know what this is! Similarly, for estimating the population total τ, here is the formula: P (| τ ^ − τ | > z α / 2 ⋅ N (N − n) σ 2 n) = α