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# Laptop Battery Life: Interpreting a $p$-Value

APSTAT-XXYS2K

When Carter bought his new laptop computer, the sales person told him that the average battery life was $5$ hours and that the number of hours of battery life is approximately normally distributed. After using the computer for a few days, Carter began to have his doubts. The next $10$ times that Carter used his computer, he kept track of how long it took for the battery to drain. The sample average was $4.25$.

Conducting a one-sided significance test, he found the $p$-value to be $0.038$.

What is the best way to interpret this $p$-value in the context of this situation?

A

A $p$-value as small as $0.038$ gives Carter good reason to doubt that the average battery life of his laptop really is $5$ hours.

B

If the average battery life really is $5$ hours, then a sample of $10$ observations having a sample mean as low as $4.25$ hours would only occur about $3.8\%$ of the time.

C

When $10$ observations are made, the battery life will be as low as $4.25$ hours in $3.8\%$ of the observations.

D

There is a $3.8\%$ chance that Carter's laptop computer battery will last for $4.25$ hours anytime he uses it.

E

Only $3.8\%$ of all laptop batteries will last as long as $5$ hours.