Triclosan is a compound often added to products such as soaps, lotions, and toothpaste. It is antimicrobial, so for that reason, its corporate producer maintained that it should help prevent staph infections among people who use products containing the compound. A scientist had a hunch that in fact, the opposite was true, i.e., that the compound actually is associated with higher incidence of staph infection. If we wanted to test whether people with a detectable level of triclosan have higher rates of carrying the staph bacteria than people without triclosan, which would be the appropriate alternative hypothesis

The appropriate alternative hypothesis is, Hₐ: p₁ - p₂ > 0.

Step-by-step explanation:

In this case it is provided that Triclosan is a compound often added to products such as soaps, lotions, and toothpaste.

Since the compound is antimicrobial its corporate producer maintained that it should help prevent staph infections among people who use products containing the compound.

But a scientist wants to test whether the compound actually is associated with higher incidence of staph infection.

That is he wants to determine whether people with a detectable level of triclosan have higher rates of carrying the staph bacteria than people without triclosan.

Denote:

Group 1: people with a detectable level of triclosan

Group 2: people without a detectable level of triclosan

To test this the hypothesis can be defined as follows:

H₀: The proportion of people with a detectable level of triclosan does not have higher rates of carrying the staph bacteria than people without triclosan, i.e. p₁ - p₂ ≤ 0.

Hₐ: The proportion of people with a detectable level of triclosan have higher rates of carrying the staph bacteria than people without triclosan, i.e. p₁ - p₂ > 0.

Thus, the appropriate alternative hypothesis is, Hₐ: p₁ - p₂ > 0.