Approach (paired t-test)
Testing whether two paired measurements, X and Y, have equal means is done in terms of the differences
D = Y - X
The test is then expressed as
H0: µD = 0
HA: µD ≠ 0
or a one-tailed variant. The hypotheses are therefore assessed with a standard univariate t-test using test statistic
This is compared to a t distribution with n - 1 degrees of freedom to find the p-value.
Example
The diagram below illustrates a 2-tailed test for equal means, based on n = 15 paired observations.
From the p-value, we conclude that there is very strong evidence that the means for Y and X are different.