Page 54 - Statistics II for Dummies

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Part I: Tackling Data Analysis and Model-Building Basics
Estimating Parameters by Using

Confidence Intervals

Confidence intervals are a statistician’s way of covering his you-know-what
when it comes to estimating a population parameter. For example, instead
of just giving a one-number guess as to what the average household income
is in the United States, a statistician gives a range of likely values for this
number. He does this because

✓ All good statisticians know sample results vary from sample to sample,
so a one-number estimate isn’t any good.
✓ Statisticians have developed some awfully nice formulas to give a range
of likely values, so why not use them?
In this section, you get the general formula for a confidence interval, including
the margin of error, and a good look at the common approach to building
confidence intervals. I also discuss interpretation and the chance of making
an error.

Getting the basics: The general
form of a confidence interval

The big idea of a confidence interval is coming up with a range of likely
values for a population parameter. The confidence level represents the
chance that if you were to repeat your sample-taking over and over, you’d get
a range of likely values that actually contains the actual population parameter.
In other words, the confidence level is the long-term chance of being correct.

The general formula for a confidence interval is

Confidence interval = Sample statistic ± Margin of error

The confidence interval has a certain level of precision (measured by the
margin of error). Precision measures how close you expect your results to be
to the truth.

For example, suppose you want to know the average amount of time a stu-
dent at The Ohio State University spends listening to music on an MP3 player
per day. The average time for the entire population of OSU students who are
MP3-player users is the parameter you’re looking for. You take a random
sample of 1,000 students and find that the average time a student uses an
MP3 player per day to listen to music is 2.5 hours, and the standard deviation
is 0.5 hours. Is it right to say that the population of all OSU-student,

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