Question

Suppose your marketing colleague used a known population mean and standard deviation to compute the standard error as 56.4 for samples of a particular size. You don't know the particular sample size but your colleague told you that the sample size is greater than 70. Your boss asks what the standard error would be if you triple the sample size.

What is the standard error for the new sample size?

Please round your answer to the nearest tenth.

Answer 1

The formula for Standard error is

$SE=\frac{\sigma}{\sqrt{n}}$

If the Sample size increases the standard error decreases. Since here if the sample size is trippled then Standard error is decreased by

$\frac{SE}{\sqrt{3}}=\frac{56.4}{\sqrt{3}}=32.56\Rightarrow 32.6$

the standard error for the new sample size is 32.6