Paired t-test for N > 30 I have 2 samples, and I want to test difference in means to see if they are related so I think I need to do a paired t-test.  There are over 60 observations in each pair.  Can one use paired t-test for N over 30?  
 A: Yes.  in fact, the larger the $N$ the better.
A: Judging from the way you've written your question you cannot use a paired t-test.  You said, "there are over 60 observations in each pair." That suggests 60 observations in each group. You probably need an independent samples t-test.  But it's hard to tell.
You use a paired samples t-test if you have matched pairs of observations in some way.  One way that's done is by taking two measures of each subject.  Those measures are paired by being within subjects.  Another way might be married couples where you're taking a measure between sexes but it's husband and wife. The samples will be paired by couple. You haven't described a scenario like that so it's likely you need an independent samples t-test.
As for the N in each group, the larger the better. And, the more similar the better.
A: It is very much valid to use the paired $t$-test as long as you have 1) data that can be paired and therefore a difference can be calculated 2) differences which are normally distributed 3) if your number of pairs is larger than 30, the $t$-distribution will approach the $z$-distribution, so either one is acceptable, but typically for large number of pairs one resorts to the $z$-distribution.  In this case the normality requirement is relaxed based on the Central Limit Theorem.
