For the given hypothesis test, explain the meaning of a Type I error, a Type II error, or a correct decision as specified.
In the past, the mean running time for a certain type of flashlight battery has been
The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result. The hypotheses are:
H
0: μ = 9.7 hours
H
a: μ > 9.7 hours
where μ is the mean running time of the new batteries . Explain the meaning of a Type I error.
◦ A Type I error would occur if, in fact, μ = 9.7 hours, but the results of the sampling do not lead to rejection of that fact.
◦ A Type I error would occur if, in fact, μ > 9.7 hours, but the results of the sampling lead to the conclusion that μ < 9.7 hours.
◦ A Type I error would occur if, in fact, μ = 9.7 hours, but the results of the sampling lead to the conclusion that μ > 9.7 hours.
◦ A Type I error would occur if, in fact, μ > 9.7 hours, but the results of the sampling fail to lead to that conclusion.
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