# Water specimens are taken from water used for cooling as it is being discharged from a power plant into a river. It has been determined that as long as the mean temperature of the discharge is at most 150F, there will be no negative effects on the river's ecosystem. To investigage whether the plant is in compliance with regulations that prohibit a mean discharge water temperature above 150F, researchers will take 50 specimens at randomly selected times and record the temperature of each specimen. The resulting data will be used to test the hypotheses: H0:μ≤150FH0:μ≤150F Ha:μ>150FHa:μ>150F. (a) In the context of this problem, describe Type I and Type II errors. Type I Error: Select an answer  A Type I error is not obtaining convincing evidence that the mean water temperature is greater than 150F when in fact it is greater than 150F.  A Type I error is obtaining convincing evidence that the mean water temperature is greater than 150F when in fact it is at most 150F.  Type II Error: Select an answer  A Type II error is obtaining convincing evidence that the mean water temperature is greater than 150F when in fact it is at most 150F.  A Type II error is not obtaining convincing evidence that the mean water temperature is greater than 150F when in fact it is greater than 150F.  (b) Which type of error would you consider more serious? Explain. Select an answer  A Type I Error is more serious, as the ecosystem will be harmed and no action will be taken.  A Type II Error is more serious, as the ecosystem will be harmed and not action will be taken.

Question
Water specimens are taken from water used for cooling as it is being discharged from a power plant into a river. It has been determined that as long as the mean temperature of the discharge is at most 150F, there will be no negative effects on the river's ecosystem. To investigage whether the plant is in compliance with regulations that prohibit a mean discharge water temperature above 150F, researchers will take 50 specimens at randomly selected times and record the temperature of each specimen. The resulting data will be used to test the hypotheses:

H0:μ≤150FH0:μ≤150F

Ha:μ>150FHa:μ>150F.

(a) In the context of this problem, describe Type I and Type II errors.

Type I Error:

A Type I error is not obtaining convincing evidence that the mean water temperature is greater than 150F when in fact it is greater than 150F.

A Type I error is obtaining convincing evidence that the mean water temperature is greater than 150F when in fact it is at most 150F.

Type II Error:

A Type II error is obtaining convincing evidence that the mean water temperature is greater than 150F when in fact it is at most 150F.

A Type II error is not obtaining convincing evidence that the mean water temperature is greater than 150F when in fact it is greater than 150F.

(b) Which type of error would you consider more serious? Explain.

A Type I Error is more serious, as the ecosystem will be harmed and no action will be taken.

A Type II Error is more serious, as the ecosystem will be harmed and not action will be taken.

Which of these statements is true about continuous random variables and their probability distributions?

1. The distribution is modeled by a probability distribution that is non-negative.
2. The probability of an individual event E is calculated by P(X=E).
3. The total area under the curve is 1.
• II only
• I and III only
• III only
• I and II only
• I only

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