Question

A power plant discharges water into a river. Regulators determine that as long as the mean temperature of the discharged water is no more than 150°F, there will be no negative effects on the river’s ecosystem. Data will be collected to test the following hypotheses:
H0: μ = 150°F
H????: μ > 150°F
(A) Describe a Type I error in the context of this problem
(B) Describe a Type II error in the context of this problem
(C) Which type of error would an environmental group consider the more serious? Explain briefly.

Answer 1

Answer:

(A) Type I error in the context of this problem is chances of regulators believing that the mean temperature of the discharged water is more than 150°F but in actual the mean temperature of the discharged water was 150°F.

(B) Type II error in the context of this problem is chances of regulators believing that the mean temperature of the discharged water is no more than 150°F but in actual the mean temperature of the discharged water was more than 150°F.

(C) An environmental group will consider the Type II error more serious.

Step-by-step explanation:

We are given that a power plant discharges water into a river. Regulators determine that as long as the mean temperature of the discharged water is no more than 150°F, there will be no negative effects on the river’s ecosystem.

We are also given with the following hypothesis;

Null Hypothesis, $H_0$ : $\mu$ = 150°F

Alternate Hypothesis, $H_a$ : $\mu$ > 150°F

(A) Type I error states that Probability of rejecting null hypothesis given the fact that null hypothesis was true or in other words Probability of rejecting a true hypothesis.

So, Type I error in the context of this problem is chances of regulators believing that the mean temperature of the discharged water is more than 150°F but in actual the mean temperature of the discharged water was 150°F.

(B) Type II error states that Probability of accepting null hypothesis given the fact that null hypothesis was false or in other words Probability of accepting a false hypothesis.

So, Type II error in the context of this problem is chances of regulators believing that the mean temperature of the discharged water is no more than 150°F but in actual the mean temperature of the discharged water was more than 150°F.

(C) An environmental group will consider the Type II error more serious because by committing Type II error they believe that the mean temperature of the discharged water is no more than 150°F and they assume that there is no negative effects on the river’s ecosystem but in reality that the mean temperature of the discharged water was more than 150°F and it is producing negative effects on the river’s ecosystem.