Question

if we need to decrease the standard deviation of the sampling distribution by half what do we need to do to the sample size

Answer 1

The answer is below

Explanation:

For a normal distributed population with a mean (μ), and a standard deviation (σ), if a sample size of n is selected from the population, the mean of the sample (
`\mu_x`) = μ and the standard deviation of the sample (
`\sigma_x`) =
`(\sigma )/(√(n) )`

Let the normal distribution population have a standard deviation of σ. If the standard deviation is to be decreased by half, the sample size (n) needed is:

`Using:\\\\\sigma_x=(\sigma)/(√(n) ) \\\\but\ \sigma_x=(\sigma)/(2)\\\\Hence:\\\\ (\sigma)/(2)=(\sigma)/(√(n) )\\\\Divide\ through\ by \ \sigma\ to\ get:\\\\ (1)/(2)=(1)/(√(n) )\\\\√(n)=2\\\\square\ both\ sides:\\\\(√(n) )^2=2^2\\\\n=4\\\\`

To decrease the standard deviation of the sampling distribution by half we need a sample size of 4