Question

In the past, the mean running time for a certain type of flashlight battery has been 9.2 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: H O : µ = 9.2 hours Ha : µ > 9.2 hours where µ is the mean running time of the new batteries 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 II error

B) Correct decision

C) Type I error

Answer 1

Solution:

   We are given that:

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.

H₀ : µ = 9.2 hours Vs H_a : µ > 9.2 hours

where µ is the mean running time of the new batteries

    we are given that: the results of the sampling lead to rejection of the null hypothesis and in fact, the mean running time has not increased.

We have to classify that conclusion as a Type I Error, Type II Error or correct decision.

Type I Error is: We reject H0 , in fact, H0 is true.

Type II Error is: We fail to reject H0 , in fact, H0 is false.

Thus from the given information, we can see that: Null hypothesis H0 is rejected and also given that: in fact, mean running time has not increased.

it means that Null hypothesis H0: µ = 9.2 hours is rejected, in fact, H0: µ = 9.2 hours is true.

Thus the conclusion stated in question is classified as Type I Error.

Thus correct option is: C) Type I Error.