playground safety $($Lesson $19)$

Regulations from the Environmental Protection Agency $($EPA$)$ say that soil used in play areas should not have lead levels that exceed $=400$

parts per million $($ppm$).$ Before beginning construction at a new site, an agent will take a sample of soil and run a significance test on the mean lead level in the soil. If the mean lead level in the sample is significantly higher than $400$ ppm then the soil is deemed unsafe and construction

must stop.

Below are the hypotheses for this test:

$H_0$:$400ppm($the soil is safe$)$

$H_a$:$>400ppm($the soil is unsafe$)$

Quesion $21$ Which of the following would be a Type I error in this context?

The soil is actually safe, so construction is allowed to continue.

The soil is actually safe and construction was stopped unnecessarily.

The soil is actually unsafe, so construction is allowed to

continue.

The soil is actually unsafe but construction was allowed to continue

and children will be put at risk of lead poisoning.

Quesion $22$ Which of the following would be a Type II error in this context?

The soil is actually unsafe, so construction is allowed to continue.

The soil is actually unsafe but construction was allowed to continue

and children will be put at risk of lead poisoning.

The soil is actually safe and construction was stopped

unnecessarily.

The soil is actually safe, so construction is allowed to continue.