In the Past, the Mean Running Time for a Certain $8.4$

question 12

Multiple Choice

In the past, the mean running time for a certain type of flashlight battery has been $8.4$ 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:
$\begin{array} { l } H _ { 0 } : \mu = 8.4 \text { hours } \\H _ { A } : \mu > 8.4 \text { hours }\end{array}$
Explain the result of a Type II error.

• A) The manufacturer will decide the mean battery life is greater than \(8.4\) hours when in fact it is greater than \(8.4\) hours.
• B) The manufacturer will decide the mean battery life is less than \(8.4\) hours when in fact it is greater than \(8.4\) hours.
• C) The manufacturer will decide the mean battery life is \(8.4\) hours when in fact it is \(8.4\) hours.
• D) The manufacturer will decide the mean battery life is \(8.4\) hours when in fact it is greater than \(8.4\) hours.
• E) The manufacturer will decide the mean battery life is greater than \(8.4\) hours when in fact it is \(8.4\) hours.

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Definitions:

Random Variable

A random variable is a variable whose possible values are numerical outcomes of a random phenomenon.

Success Probability

The likelihood or chance of a particular event or outcome happening, often expressed in terms of percentage or decimal.

Poisson Random Variable

A statistical measure that expresses the probability of a given number of events occurring in a fixed interval of time or space, assuming these events happen with a known constant mean rate and independently of the time since the last event.

Specified Interval

A defined range of values within which a particular parameter or statistic is expected to lie.