t-test for differently-sized sample sets First, Please understand my lack of English skills.
I have a problem dealing with statistical hypothesis testing.
I'm in a situation to evaluate two independent samples t-test. There are two different-sized sample sets and these sets are sampled using method A & B (for method A, $n= 100$, and for method B, $n= 1000$). I collected data for 22 days.
I had two questions about people who used method A vs. method B to purchase the same item.


*

*(Number of purchases) : Did people using method A purchase more of the item than people using method B?
In this case, how can I perform a reasonable comparison?
My problem is that there are 10 times more transactions from method B than from method A.

*(cumulative sales aspect) : Did the people using method A spend more money on the item than people using method B?
How can I perform a reasonable comparison in this case?
 A: The general rule of thumb is that once $n$ gets above 30, it is reasonable to approximate it with the normal distribution. So 100 is large enough, and 1000 is way beyond the minimum. 
If your null hypothesis is that the mean and variance are the same, and the alternative hypothesis is that the means and variances are different, then take the difference between the sample means and divide by the observed standard deviation, and use that as your $z-value$. To find the observed standard deviation, take $\sqrt{\frac {s_1^2}{n_1}+\frac {s_2^2}{n_2}}$, where $n_1$ and $n_2$ are the sample sizes and $s_1$ and $s_2$ are the sample standard deviations.
See https://www.stat.colostate.edu//~vollmer/stat307pdfs/book_ch18.pdf
If your null hypothesis is that the mean and variance are the same, and the alternative hypothesis is that the means are different but the variance is the same, then you can take $s_1=s_2=s$ where $s$ is the sample standard deviation over all the samples. Then you can factor out $s$ to get $s\sqrt{\frac {1}{n_1}+\frac {1}{n_2}}$.
BTW, the 't' in "t-test" is lowercase.
