Question

A sample of n = 16 scores has a mean of M = 40 and a variance of s2 = 64. What is the estimated standard error for the sample mean?

Answer 1

Answer:

$S.E = 2$

Step-by-step explanation:

Given

$Mean = 40$

$s^2 = 64$ ----- variance

$n = 16$ ------------ sample

Required

Determine the S.E

The estimated standard error (S.E) for the sample mean is calculated using the following formula:

$S.E = \frac{SD}{\sqrt n}$

Where

$SD = Standard\ Deviation$

$SD = \sqrt {s^2}$

$SD = \sqrt {64}$

$SD = 8$

So:

$S.E = \frac{SD}{\sqrt n}$

$S.E = \frac{8}{\sqrt{16}}$

$S.E = \frac{8}{4}$

$S.E = 2$

Hence: the estimated standard error for the sample mean is 2