One sample has n = 5 scores and the second has n = 10 scores.If the pooled variance for the two sample is 30,then what is the value of the estimated standard error for the sample mean difference?
A)The square root of (30/15)
B)The square root of (60/15)
C)The square root of (30/5 + 30/10)
D)The square root of (30/4 + 30/9)

Question

One sample has n = 5 scores and the second has n = 10 scores.If the pooled variance for the two sample is 30,then what is the value of the estimated standard error for the sample mean difference?​
A)​The square root of (30/15)
B)​The square root of (60/15)
C)​The square root of (30/5 + 30/10)
D)​The square root of (30/4 + 30/9)

Quizplus · Accepted Answer

The formula for the estimated standard error for the sample mean difference is:

SE = sqrt[ (s1^2/n1) + (s2^2/n2) ]

where s1^2 and s2^2 are the sample variances for the two groups, and n1 and n2 are the sample sizes.

In this case, we have:

s1^2 = s2^2 = 30 (since we are given the pooled variance)
n1 = 5
n2 = 10

Substituting these values into the formula, we get:

SE = sqrt[ (30/5) + (30/10) ]
SE = sqrt[ 6 + 3 ]
SE = sqrt[ 9 ]
SE = 3

Therefore, the estimated standard error for the sample mean difference is 3. Answer choice C is the only option that matches this calculation.

One Sample Has N = 5 Scores and the Second