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Chapter 3: Building Confidence and Testing Models
essence, accounting for all of the other samples out there that it could have
gotten by building in the margin of error (±3 percent). The organization wants
to cover its bases on 95 percent of those other situations, and the ±3 percent
satisfies that.
Another way of thinking about the confidence interval is to say that if the
organization sampled 1,200 people over and over again and made a confi-
dence interval from its results each time, 95 percent of those confidence
intervals would be right. (You just have to hope that yours is one of those
right results.)
Using stat notation, you can write confidence levels as 1 – α. So if you want
95 percent confidence, you write it as 1 – 0.05. The number that α represents
is the chance that your confidence interval is one of the wrong ones. This
number, α, is also related to the chance of making a certain kind of error with
a hypothesis test, which I explain in the hypothesis-testing section.
Setting Up and Testing Models 57
A model is an equation that attempts to describe how a population behaves.
It can be a claim that’s made about a population parameter; for example, a
shipping company might say that its packages are on time 95 percent of the
time, or a campus official claims that 75 percent of students live off campus.
It is important to test these models to see whether they actually hold up in
the population, which you can do by using hypothesis tests.
In this section, you see the big ideas of hypothesis testing that are the basis
for the data-analysis techniques in this book. You review and expand on the
concepts involved in a hypothesis test, including the hypotheses, the test
statistic, and the p-value.
What do Ho and Ha represent — really?
The big idea here is that you set up a hypothesis test to see whether your
model fits the population, based on your data. In the intro stat course, you
tested simple hypotheses — like whether the population mean is equal to
ten. At the intermediate statistics level, you get to look at much more sophis-
ticated and relevant models that involve several variables and/or several
different populations in a variety of situations. The good news, though, is
that the basic ideas from intro stats apply here as well. (If you need a brief
refresher before barreling through this section, feel free to flip through your
intro stats book or check out my other book Statistics For Dummies [Wiley].)