A manufacturer of medication for migraine headaches knows that their product can damage the stomach if taken too often. Imagine that by a standard measuring process, the average damage is μ = 48.

A modification of their product is being contemplated, and based on ten trials, it is found that X¯ = 46.

Assuming σ = 5, they test H0 : μ ≥ 48, the idea being that if they reject, there is convincing evidence that the average amount of damage is less than 48.

Then Z = 46−48 5/

√

10 = −1.3.

With α = .05, the critical value is −1.645, so they do not reject because Z is not less than the critical value. What might be wrong with accepting H0 and concluding that the modification results in an average amount of damage greater than or equal to 48?