Originally Posted by

**theodds** A couple of quick points:

(1) Your null hypothesis makes no sense. Hypotheses are formulated about parameters, not statistics. It should probably read $\displaystyle \mu_1 - \mu_2 = 0$ where \mu_i is the mean during the i'th week.

(2) Run this as a paired T-Test, not a two sample T-Test. I don't think you can push through the usual distributional results with that general covariance structure for the two sample test, but the paired T-Test should be unaffected (and it should be more powerful in general, anyways).