AP Statistics 2017

(Marvins-Underground-K-12) #1

the average height of the students in our sample to estimate the true average height of the population from
which the sample was drawn. In the real world, we often are interested in some characteristic of a
population (e.g., what percentage of the voting public favors the outlawing of handguns?), but it is often
too difficult or too expensive to do a census of the entire population. The common technique is to select a
random sample from the population and, based on an analysis of the data, make inferences about the
population from which the sample was drawn. Chapters 11 – 14 of this book are primarily concerned with
inferential statistics.


Parameters versus Statistics


Values that describe a sample are called statistics , and values that describe a population are called
parameters . In inferential statistics , we use statistics to estimate parameters . For example, if we
draw a sample of 35 students from a large university and compute their mean GPA (that is, the grade point
average, usually on a 4-point scale, for each student), we have a statistic . If we could compute the mean
GPA for all students in the university, we would have a parameter .


Collecting Data: Surveys, Experiments, Observational Studies


In the preceding section, we discussed data analysis and inferential statistics. A question not considered
in many introductory statistics courses (but considered in detail in AP Statistics) is how the data are
collected. Oftentimes we are interested in collecting data in order to make generalizations about a
population. One way to do this is to conduct a survey . In a well-designed survey, you take a random
sample of the population of interest, compute statistics of interest (like the proportion of baseball fans in
the sample who think Pete Rose should be in the Hall of Fame), and use those to make predictions about
the population.
We are often more interested in seeing the reactions of persons or things to certain stimuli. If so, we
are likely to conduct an experiment or an observational study . We discuss the differences between
these two types of studies in Chapter 8 , but both basically involve collecting comparative data on groups
(called treatment and control ) constructed in such a way that the only difference between the groups
(we hope) is the focus of the study. Because experiments and observational studies are usually done on
volunteers, rather than on random samples from some population of interest (it’s been said that most
experiments are done on graduate students in psychology), the results of such studies may lack
generalizability to larger populations. Our ability to generalize involves the degree to which we are
convinced that the only difference between our groups is the variable we are studying (otherwise some
other variable could be producing the responses).
It is extremely important to understand that data must be gathered correctly in order to have analysis
and inference be meaningful. You can do all the number crunching you want with bad data, but the results
will be meaningless.
In 1936, the magazine The Literary Digest did a survey of some 10 million people in an effort to
predict the winner of the presidential election that year. They predicted that Alf Landon would defeat
Franklin Roosevelt by a landslide, but the election turned out just the opposite. The Digest had correctly
predicted the outcome of the preceding five presidential elections using similar procedures, so this was
definitely unexpected. Its problem was not in the size of the sample it based its conclusions on. Its
problem was in the way it collected its data—the Digest simply failed to gather a random sample of the
population. It turns out that its sampling frame (the population from which it drew its sample) was
composed of a majority of Republicans. The data were extensive (some 2.4 million ballots were
returned), but they weren’t representative of the voting population. In part because of the fallout from this

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