In the past, the mean running time for a certain type of flashlight battery has been 9.8 hours. 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:
$\mathrm { H } _ { 0 } : \mu = 9.8$ hours
$\mathrm { H } _ { \mathrm { a } } : \mu 9.8 \text { hours }$
Suppose that the results of the sampling lead to rejection of the null hypothesis. Classify that conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean running time has not increased.
A) Type I error
B) Type II error
C) Correct decision

Question

In the past, the mean running time for a certain type of flashlight battery has been 9.8 hours. 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: 
$\mathrm { H } _ { 0 } : \mu = 9.8$ hours
$\mathrm { H } _ { \mathrm { a } } : \mu > 9.8 \text { hours }$
 Suppose that the results of the sampling lead to rejection of the null hypothesis. Classify that conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean running time has not increased.
A) Type I error
B) Type II error
C) Correct decision

Quizplus · Accepted Answer

Rejecting the null hypothesis when it is actually true is a Type I error.

In the Past, the Mean Running Time for a Certain H0:μ=9.8\mathrm { H } _ { 0 } : \mu = 9.8H0​:μ=9.8

In the Past, the Mean Running Time for a Certain $\mathrm { H } _ { 0 } : \mu = 9.8$