Question

A researcher has a strange habit to use a sample size between √? 3
and √? 2, where? is the size of the population that she investigates. Under what circumstances, do you suggest
her to use a correction factor for the variance of the sampling distribution while estimating a
confidence interval for the population mean? What if she does not take your suggestion
seriously? Describe the potential problems involved.

Answer 1

• We should use a correction factor for the variance of the sampling distribution when more than 5% of the population is being sampled and the population has a known population size.

In this case, we nee to apply the correction factor as below.

The variance of the sampling distribution with finite population size and large sample size is,

(sigma/sqrt of N)*((N-n)/(n-1))

• she does not take your suggestion seriously (that is n > 0.05N) , then we sample a larger number of observations and the sample observations are not independent of each other.
• The Central Limit Theorem doesn’t hold and the variance of the estimate will be too big.

  e.g. the mean or proportion