Question

If you wanted to halve the standard error from Part C, what approximate sample size would you need? Why is this only approximate? *standard error of the mean = 4.31 and my sample size was 30

Answer 1

The formula of standard error ( SE) of the sample mean is as follows:

Where n is the sample size and is the standard deviation.

If we want to halve the standard error then we need to divide SE by 2

So we get

That is we need to increase sample size four times.

so new sample size = 4*n = 4*30 = 120

It is approximate because the sample provide the estimates of the parameters and not exact parameter values.