If you wish to test whether a population mean is lower than some hypothesized value, you would apply:

Testing whether a population mean is lower than a hypothesised value needs a one-tailed test with the rejection region in one tail.

A two-tailed test checks for a difference in either direction, not a specific lower value.

A half-tailed test is not a recognised statistical procedure.

A three-tailed test likewise does not exist in hypothesis testing.

The directional wording lower than fixes the critical region in the left tail alone.

One-tailed tests give greater power to detect an effect in the predicted direction.