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:
H0 : µ = 9.8 hours
Ha : µ > 9.8 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
D. Can not be determined from this information
i'm confused between A and D
Agreed, type II error.
It is a Type I error.
definetly type 1 error
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
The correct answer is A. Type I error.
A Type I error occurs when the null hypothesis is rejected, even though it is true. In this case, if the null hypothesis is actually true (i.e., the mean running time has not increased), but the test leads to rejecting the null hypothesis, then it would be a Type I error.
On the other hand, a Type II error would occur if the null hypothesis is not rejected, even though it is false. It means that the test fails to detect a true difference.
Option D cannot be the correct answer because the question states that the null hypothesis was rejected. Hence, it is possible to determine that a Type I error has occurred in this scenario.