I go confused about what I read about the t test:
We calculate the t statistic (obtained), which "represents the number of standard deviation units (or standard error units) that our sample mean is from the hypothesized value of µY, assuming the null hypothesis is true" (Frankfort-Nachmias and Leon-Guerrero 2011:266).
Let's say we compare sample A with B, I first thought the t test would perform this by comparing the means like so:
A <--> B. However after reading the above I looks like the t test compares them by
A <--> population mean <--> B. So does it calculate the difference in standard error between the two samples by comparing the mean of A en B or by comparing the difference in standard error relative to the population mean?
*Please provide a detailed explanation I'm new in statistics