In the past, the mean running time for a certain type of flashlight battery has been $8.3$ 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:
$\begin{array} { l }
H _ { 0 } : \mu = 8.3 \text { hours } \
H _ { A } : \mu 8.3 \text { hours }
\end{array}$
Explain the result of a Type I error.
A) The manufacturer will decide the mean battery life is less than $8.3$ hours when in fact it is greater than $8.3$ hours.
B) The manufacturer will decide the mean battery life is greater than $8.3$ hours when in fact it is less than $8.3$ hours.
C) The manufacturer will decide the mean battery life is greater than $8.3$ hours when in fact it is greater than $8.3$ hours.
D) The manufacturer will decide the mean battery life is $8.3$ hours when in fact it is greater than $8.3$ hours.
E) The manufacturer will decide the mean battery life is greater than $8.3$ hours when in fact it is $8.3$ hours.

Question

In the past, the mean running time for a certain type of flashlight battery has been $8.3$ 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:
$\begin{array} { l } 
H _ { 0 } : \mu = 8.3 \text { hours } \
H _ { A } : \mu > 8.3 \text { hours }
\end{array}$
Explain the result of a Type I error.
A) The manufacturer will decide the mean battery life is less than $8.3$ hours when in fact it is greater than $8.3$ hours.
B) The manufacturer will decide the mean battery life is greater than $8.3$ hours when in fact it is less than $8.3$ hours.
C) The manufacturer will decide the mean battery life is greater than $8.3$ hours when in fact it is greater than $8.3$ hours.
D) The manufacturer will decide the mean battery life is $8.3$ hours when in fact it is greater than $8.3$ hours.
E) The manufacturer will decide the mean battery life is greater than $8.3$ hours when in fact it is $8.3$ hours.

Quizplus · Accepted Answer

A Type I error occurs when the null hypothesis ($H_0$) is rejected when it is actually true. In this scenario, rejecting $H_0$ means incorrectly concluding that the mean battery life has increased (is greater than $8.3$ hours) when in reality, it has not changed and remains at $8.3$ hours.

In the Past, the Mean Running Time for a Certain 8.38.38.3

In the Past, the Mean Running Time for a Certain $8.3$