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Part IV: Guesstimating and Hypothesizing with Confidence
Rejecting H when you shouldn’t is called a type-1 error. I don’t really like this
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name, because it seems so nondescript. I prefer to call a type-1 error a false
alarm. In the case of the packages, if the consumer group made a type-1 error
when it rejected the company’s claim, they created a false alarm. What’s the
result? A very angry delivery company, I guarantee that!

To reduce the chance of false alarms, set a low cutoff probability (significance
level) for rejecting H . Setting it to 5% or 1% will keep the chance of a type-1
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error in check.
Missing out on a detection: Type-2 errors
On the other hand, suppose the company really wasn’t delivering on its
claim. Who’s to say that the consumer group’s sample will detect it? If the
actual delivery time is 2.1 days instead of 2 days, the difference would be
pretty hard to detect. If the actual delivery time is 3 days, even a fairly small
sample would probably show that something’s up. The issue lies with those
in-between values, like 2.5 days.
If H is indeed false, you want to find out about it and reject H . Not rejecting H
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when you should have is called a type-2 error. I like to call it a missed detection.
Sample size is the key to being able to detect situations where H is false and,
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thus, avoiding type-2 errors. The more information you have, the less vari-
able your results will be (see Chapter 11) and the more ability you have to
zoom in on detecting problems that exist with a claim made by H .
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This ability to detect when H is truly false is called the power of a test. Power
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is a pretty complicated issue, but what’s important for you to know is that
the higher the sample size, the more powerful a test is. A powerful test has a
small chance for a type-2 error.
As a preventative measure to minimize the chances of a type-2 error, statisti-
cians recommend that you select a large sample size to ensure that any differ-
ences or departures that really exist won’t be missed.

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