The manufacturer of a medication designed to lower blood pressure claims that the mean systolic blood pressure for people taking their medication is less than 135.

To test this claim, blood pressure is measured for a sample of 500 people who are taking the medication. The P-value for testing H0: μ = 135 versus H1: μ < 135 is P = 0.001.

a. The manufacturer concludes that because the P-value is very small, we can be fairly certain that the mean pressure is less than 135, but we cannot conclude that it is a lot smaller. Is this conclusion justified?

b. Someone else says that because the P-value is very small, we can conclude that the mean pressure is a lot less than 135.

Is this conclusion justified?