Question

A random sample is taken from a large population and a mean calculated for the quantity of interest Which one of the following does NOT have an effect on the accuracy of the estimate of the mean value of the quantity of interest in the population?

Size of the sample

Variance of the quantity of interest in the population

Size of the population

Whether some of the sample have been sampled more than once

Answer 1

Sampling with replacement does not affect the accuracy of the estimate of the mean value of the quantity of interest in the population.

Step-by-step explanation:

The size of the sample, n, that is required in order to be large enough depends on the original population from which the samples are drawn. If the original population is far from normal, then more observations are needed for the sample means or sums to be normal. Sampling is done with replacement.

If some of the sample have been sampled more than once, it will not affect the accuracy of the estimate of the mean value of the quantity of interest in the population. Each observation in the sample contributes to the estimate of the mean, regardless of whether it has been sampled multiple times.