# Compute the total number of weeks for two alternatively running tests to obtain sufficient coverage

I have two tests running alternatively in each week. Every time a test is selected with 0.50 probability and runs for an hour. Each test provides a "profit" that it makes within that hour. What I need is to compare the performance of both tests that run within the same hour on the same weekday (e.g. 6pm-7pm on Monday) so a paired t-test might be appropriate here. The question is, how many weeks are enough for me to get sufficient overlap for both tests covering an entire week? I know the coverage is >=50% for sure but I just couldn't figure out how to compute it within the following weeks. Could it be close to 100% from time to time? Thanks!

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Why would you "compute the time length" of a run, when you say, "runs for an hour." Why would knowing the "time length" give you any way to "obtain sufficient coverage?" This question definitely needs clarification. –  Thomas Andrews Nov 7 '12 at 19:26
I meant "total number of weeks" for both tests running. –  Rock Nov 7 '12 at 19:28
With what certainty do you want the result? There is no amount of time to ensure that both tests have run in every hour of every day of the week. –  Thomas Andrews Nov 7 '12 at 19:31
@ThomasAndrews Each test provides profit that it makes within that hour and I might need a paired t-test to see whether a test is better (makes more profit) than the other. –  Rock Nov 7 '12 at 19:33
@ThomasAndrews What you are saying is it's not possible for each test covers the entire week? What about a certain percentage (e.g. 90%) of the week? I know it's >=50% for sure but I just couldn't figure out how to compute the coverage within the continuous weeks. Could it be close to 100% from time to time? –  Rock Nov 7 '12 at 19:41