What is a statistical test?
A statistical test is a procedure used to decide if an assertion (often called a hypothe-
sis) about a population’s chosen quantitative feature is true or false. These tests usual-
ly entail drawing on a random sample (or simple random sample) from the chosen
population, then calculating a statistic about the chosen feature. From the result, a
statistician can usually determine if the hypothesis is true, false, rare, common, or
something in between. Overall, for a statistical test to be valid, it is necessary to
choose what statistic to use, what sample size, and what criteria to use for rejection or
acceptance of the tested hypothesis.
How is statistical data presented?
There are many ways to present statistical data, all of which involve graphical means
to translate the results of statistical tests. A histogramis a graphical representation of
a distribution function using rectangles. It is also most often constructed from a fre-
quency table (see below). The widths of the rectangles usually indicate the intervals
into which the range of observed values are divided; the heights of the rectangles indi-
cate the number of observations that occur in each interval. The shapes of histograms
vary depending on the chosen size of the intervals. 263
APPLIED MATHEMATICS
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In this example of a cumulative distribution chart, all students (100 percent) fall within the maximum score of
100, while smaller numbers of students fall within each progressively lower score on a test.