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 discharged water is at most 150°F, there will be no negative effects on the river's ecosystem. To investigate whether the plant is in compliance with regulations that prohibit a mean discharge water temperature above 150°F, a scientist will take 50 water specimens at randomly selected times and will record the water temperature of each specimen. She will then use a z statistic z = x − 150 σ n (b) Describe Type I and Type II errors in this context. (Select all that apply.) A Type I error is obtaining convincing evidence that the mean water temperature is greater than 150°F when in fact it is greater than 150°F. A Type II error is not obtaining convincing evidence that the mean water temperature is greater than 150°F when in fact it is greater than 150°F. A Type II error is obtaining convincing evidence that the mean water temperature is greater than 150°F when in fact it is (at most) 150°F. A Type I error is obtaining convincing evidence that the mean water temperature is greater than 150°F when in fact it is (at most) 150°F. A Type I error is not obtaining convincing evidence that the mean water temperature is greater than 150°F when in fact it is greater than 150°F. (c) The rejection of H0 when z ≥ 1.9 corresponds to what value of α? (That is, what is the area under the z curve to the right of 1.9?) (Round your answer to four decimal places.) α =
Continuous Probability Distributions
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Normal Distribution
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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 discharged water is at most 150°F, there will be no negative effects on the river's ecosystem. To investigate whether the plant is in compliance with regulations that prohibit a mean discharge water temperature above 150°F, a scientist will take 50 water specimens at randomly selected times and will record the water temperature of each specimen. She will then use a z statistic
z =
x − 150
σ
n
(b)
Describe Type I and Type II errors in this context. (Select all that apply.)
A Type I error is obtaining convincing evidence that the mean water temperature is greater than 150°F when in fact it is greater than 150°F.
A Type II error is not obtaining convincing evidence that the mean water temperature is greater than 150°F when in fact it is greater than 150°F.
A Type II error is obtaining convincing evidence that the mean water temperature is greater than 150°F when in fact it is (at most) 150°F.
A Type I error is obtaining convincing evidence that the mean water temperature is greater than 150°F when in fact it is (at most) 150°F.
A Type I error is not obtaining convincing evidence that the mean water temperature is greater than 150°F when in fact it is greater than 150°F.
(c)
The rejection of
H0 when z ≥ 1.9
corresponds to what value of α? (That is, what is the area under the z curve to the right of 1.9?) (Round your answer to four decimal places.)
α =
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