Page 40 - Statistics II for Dummies

24 Part I: Tackling Data Analysis and Model-Building Basics

The sampling variability is measured by the margin of error (the amount that
you add and subtract from your sample statistic), which for this sample is
only about 0.5 percent. (To find out how to calculate margin of error, turn to
Chapter 3.) That means that the estimated percentage of female Democrats
in the U.S. voting population is somewhere between 35.5 percent and 36.5
percent.

The margin of error, combined with the sample proportion, forms what stat-
isticians call a confidence interval for the population proportion. Recall from
Stats I that a confidence interval is a range of likely values for a population
parameter, formed by taking the sample statistic plus or minus the margin of
error. (For more on confidence intervals, see Chapter 3.)

Comparing proportions

Researchers, the media, and even everyday folk like you and me love to com-
pare groups (whether you like to admit it or not). For example, what propor-
tion of Democrats support oil drilling in Alaska, compared to Republicans?
What percentage of women watch college football, compared to men? What
proportion of readers of Statistics II For Dummies pass their stats exams with
flying colors, compared to nonreaders?

To answer these questions, you need to compare the sample proportions
using a hypothesis test for two proportions (see Chapter 3 or your Stats I
textbook).

Suppose you’ve collected data on a random sample of 1,000 voters in the U.S.
and you want to compare the proportion of female voters to the proportion
of male voters and find out whether they’re equal. Suppose in your sample
you find that the proportion of females is 0.53, and the proportion of males
is 0.47. So for this sample of 1,000 people, you have a higher proportion of
females than males.

But here’s the big question: Are these sample proportions different enough to
say that the entire population of American voters has more females in it than
males? After all, sample results vary from sample to sample. The answer to
this question requires comparing the sample proportions by using a hypoth-
esis test for two proportions. I demonstrate and expand on this technique in
Chapter 3.

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