How does the t ratio do this?
The t test sets up a sampling distribution of means with a mean that is specified by the Null Hypothesis (m).

The t test calculates if your sample mean is far in the tails of the sampling distribution and far away from the population mean (m).

If it is, the difference may be too big to be chance. If your group was really from the Null Hypothesis distribution, then the difference (and your t-score) should be close to zero.

The t-score is made a relative score by dividing the difference between the sample mean and m by the standard error of the mean. See your book for the standard error formula.

That's how we know if your sample mean is rare by chance as we can calculate the areas in the tails.