An independent-measures study with n = 6 in each sample, produces a sample mean

difference of 4 points and a pooled variance of 12. What is the value for the t statistic?
a. 1
b. 2
c. 4/√2
d. 4/√8

To find the value for the t statistic in this scenario, we need to use the formula:

t = (x̄1 - x̄2) / √((s1² / n1) + (s2² / n2))

Where:
x̄1 - x̄2 is the sample mean difference (4 points),
s1 is the standard deviation of the first sample (which is equal to the square root of the pooled variance, so s1 = √12),
n1 is the sample size of the first sample (6 in this case),
s2 is the standard deviation of the second sample (also equal to √12),
n2 is the sample size of the second sample (also 6 in this case).

Substituting these values into the formula gives:

t = (4) / √((√12² / 6) + (√12² / 6))

Simplifying this expression further:

t = 4 / √(12/6 + 12/6)
= 4 / √(2 + 2)
= 4 / √4
= 4 / 2
= 2

Therefore, the value for the t statistic in this case is 2. So, the correct answer is option b.