Page 60 - Statistics II for Dummies

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Part I: Tackling Data Analysis and Model-Building Basics
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 confidence
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. Here, α represents the chance
that your confidence interval is one of the wrong ones. This number, α, is also
related to the random chance of making a certain kind of error with a hypothe-
sis test, which I explain in the later section “False alarms and missed opportu-
nities: Type I and II errors.”

What’s the Hype about Hypothesis Tests?

Suppose a shipping company claims that its packages are on time 92 percent of
the time, or a campus official claims that 75 percent of students live off campus.
If you’re questioning these claims, how can you use statistics to investigate?
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 Ho and Ha really represent

You use a hypothesis test in situations where you have a certain model in
mind and want to see whether that model fits your data. Your model may
be one that just revolves around the population mean (testing whether that
mean is equal to ten, for example). Your model may be testing the slope of
a regression line (whether or not it’s zero, for example, with zero meaning
you find no relationship between x and y). You may be trying to use several
different variables to predict the marketability of a product, and you believe
a model using customer age, price, and shelf location can help predict it,
so you need to run one or more hypothesis tests to see whether that model
works. (This particular process is called multiple regression, and you can
find more info on it in Chapter 5.)

A hypothesis test is made up of two hypotheses:

✓ The null hypothesis, Ho: Ho symbolizes the current situation — the one
that everyone assumed was true until you got involved.
✓ The alternative hypothesis, Ha: Ha represents the alternative model
that you want to consider. It stands for the researcher’s hypothesis, and
the burden of proof lies on the researcher.

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