In the past, the mean lifetime for a certain type of flashlight battery has been lower than desired. The manufacturer has introduced a change in the production method and wants to perform a significance test to determine whether the mean lifetime has increased as a result. The hypotheses are: H0: μ = 9.6 hours Ha: μ > 9.6 hours Suppose that the results of the sample lead to nonrejection of the null hypothesis.

a) Classify that conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean running time has increased.

Question

Mathematics

Greyson

10 November, 18:53

In the past, the mean lifetime for a certain type of flashlight battery has been lower than desired. The manufacturer has introduced a change in the production method and wants to perform a significance test to determine whether the mean lifetime has increased as a result. The hypotheses are: H0: μ = 9.6 hours Ha: μ > 9.6 hours Suppose that the results of the sample lead to nonrejection of the null hypothesis.

a) Classify that conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean running time has increased.

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Answers (1)

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Alma Willis · Answer 1

Step-by-step explanation:

Type I error occurs if the null hypothesis is rejected when in the real sense, it is actually true.

Type II error occurs if the null hypothesis is not rejected when in the real sense, it is actually false.

The null hypothesis is

H0: μ = 9.6 hours

The alternative hypothesis is

Ha: μ > 9.6

Suppose that the results of the sample lead to non rejection of the null hypothesis if in fact the mean running time has increased it means that

a) the conclusion is a type I error because the null hypothesis was of rejected even though it was false