Statistics and probabilities

Question

If you are performing a matched pairs t-test and you have a critical value of +/-2.131 for an alpha = .05, how many participants did you recruit?

Answer 1

for alpha = .05 and t = ±2.31, we have 8 df. In Excel, for example, =T.INV.2T(0.05,8) returns a value of 2.306004

Then, as we have 8 degrees of freedom, we have 9 pairs (a paired t test is equivalent to a 1 group t-test of the mean equaling 0). Then, we need 9 pairs, or 9*2 = 18 participants.