Question

suppose someone is tested for an viral infection. the lab is looking for evidence that the person is infected, so it can be said that they are conducting a hypothesis test using the null and alternative hypotheses of

$h_0$: the person is healthy.

$h_a$: the person is infected.

if there is a type 1 error, then...select the one best answer

the person is infected, but the test says they are healthy.
the person is healthy, but the test says they are infected.
the test is inconclusive-- we dont know if they are infected.

if there is a type 2 error, then...select the one best answer

the person is infected, but the test says they are healthy.
the person is healthy, but the test says they are infected.
the test is inconclusive-- we dont know if they are infected.

Explanation:

A Type 1 error occurs when the null hypothesis ($H_0$) is true but is rejected. Here, $H_0$ is that the person is healthy. So a Type 1 error means the person is healthy but the test says they are infected. A Type 2 error occurs when the alternative hypothesis ($H_A$) is true but the null hypothesis is not rejected. Here, $H_A$ is that the person is infected, so a Type 2 error means the person is infected but the test says they are healthy.

Answer:

For Type 1 error: The person is healthy, but the test says they are infected.
For Type 2 error: The person is infected, but the test says they are healthy.