Presbycusis is the gradual hearing loss that occurs as a person ages. An estimated one-quarter of Americans between the ages of 65 and 75 and three-quarters of those older than 75 have some degree of hearing loss. An audiologist is interested in the efficacy of three different types of hearing aids. He gathers three groups of hearing-impaired clients: One group receives analog hearing aids, which convert sound waves into amplified electrical signals. The second group receives digital hearing aids, which use directional microphones to control the flow of sound and convert the sound waves into numerical codes before amplifying them. The third group receives cochlear implants. The results come in, and a statistician conducts an analysis of variance.

The is that there is no difference between the population means (in other words, there is no treatment effect).
The is that at least one of the population means is different from another (in other words, there is an effect of at least one of the treatments).