Question

Q17 What is meant when a sample statistic is said to be an unbiased estimator? [2 Marks]

DO NOT WRITE THE ANSWER - USE WORD FORMAT.

NO PLAGIARISM PLEASE

Answer 1

A statistic is said to be an unbiased estimate of a given parameter when the mean of the sampling distribution of that statistic can be shown to be equal to the parameter being estimated.

For example, the mean of a sample is an unbiased estimate of the mean of the population from which the sample was drawn.

s² calculated on a sample is an unbiased estimate of the variance of the population from which the sample was drawn.

s² divided by n (the size of the sample) is an unbiased estimate of the variance of the sampling distribution of means for random samples of size n and the square root of this quantity is called the standard error of the mean. It is a commonly used index of the error entailed in estimating a population mean based on the information in a random sample of size n.