Question

Two samples, each with n = 5 scores, have a pooled variance of 40. What is the estimated standard error for the sample mean difference?​

Answer 1

The estimated standard error for the sample mean difference is 4.

Step-by-step explanation:

The estimated standard error for the sample mean difference can be calculated using the formula:

SE = √[(s1^2)/n1 + (s2^2)/n2]

where s1 and s2 are the standard deviations of the two samples and n1 and n2 are the sample sizes.

In this case, the two samples have the same size (n = 5) and the pooled variance is 40, which represents the average of the variances of the two samples. Therefore, the estimated standard error for the sample mean difference is:

SE = √[(40/5 + 40/5)] = √[8 + 8] = 4.

Answer 2

Answer: 25.30

Step-by-step explanation:

Given : Sample size of both samples : n= 5

A pooled variance :
`S_p=40`

The formula to find the standard error for the sample mean difference is given by :-

`S.E.=S_p\sqrt{(1)/(n_1)+(1)/(n_2)}\\\\\Rightarrow\ S.E.=(40)\sqrt{(1)/(5)+(1)/(5)}\\\\\Rightarrow\ S.E.=(40)\sqrt{(2)/(5)}=25.2982212813\approx25.30`

Therefore, the estimated standard error for the sample mean difference is 25.30