A researcher has a strange habit to use a sample size between √? and √?, where...

A researcher has a strange habit to use a sample size between √? and √?, 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.

Expert Solution

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.

if 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 (e.g. the mean or proportion) will be too big. The potential problems involved would be high standard errors of the population mean and unreliable confidence interval estimates.

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,

where is the population standard deviation and n is the sample size.

orchestra answered 2 years ago

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