Water specimens are taken from water used for cooling as it is being discharged
ID: 3364150 • Letter: W
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 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 =
to decide between the hypotheses
H0: = 150 and Ha: > 150,
where is the mean temperature of discharged water. Assume that is known to be 10.
(A) Explain why use of the z statistic is appropriate in this setting.
We can use z as we know the population mean.
We can use z as we know the sample size.
We can use z as we know the population standard deviation.
We can use z as we know the population size.
We can use z as we know the sample standard deviation.
(B) Describe Type I and Type II errors in this context. (Select all that apply.)
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.
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 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 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 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.
x 150 nExplanation / Answer
(A)
We can use z as we know the population standard deviation i.e. sigma = 10
(B)
A type I error is the incorrect rejection of a true null hypothesis
while a type II error is incorrectly retaining a false null hypothesis
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.
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