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

Answer:

The answer is below

Step-by-step 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 ($\sigma_x$) = $\frac{\sigma }{\sqrt{n} }$

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:

$Using:\\\\\sigma_x=\frac{\sigma}{\sqrt{n} } \\\\but\ \sigma_x=\frac{\sigma}{2}\\\\Hence:\\\\ \frac{\sigma}{2}=\frac{\sigma}{\sqrt{n} }\\\\Divide\ through\ by \ \sigma\ to\ get:\\\\ \frac{1}{2}=\frac{1}{\sqrt{n} }\\\\\sqrt{n}=2\\\\square\ both\ sides:\\\\(\sqrt{n} )^2=2^2\\\\n=4$

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