Question

The data from an independent-measures research study produce a sample mean difference of 4 points and a pooled variance of 18. If there are n = 4 scores in each sample, what is the estimated standard error for the sample mean difference?​

Answer 1

Answer: 3

Step-by-step explanation:

Given : Pooled variance : $\sigma^2=18$

Sample sizes of each sample = $n_1=n_2=4$

We know that the standard error for the sample mean difference is given by :-

$S.E.=\sqrt{\sigma^2(\dfrac{1}{n_1}+\dfrac{1}{n_2})}\\\\=\sqrt{(18)(\dfrac{1}{4}+\dfrac{1}{4})}\\\\=\sqrt{(18)(\dfrac{1}{2})}=\sqrt{9}=3$

Hence, the estimated standard error for the sample mean difference =3