XULAneXUS: Xavier University of Louisiana’s Undergraduate Research Journal.
Scholarly Note. Vol. 5, No. 1, April 2008
Application of the Paired t-test
Stephanie D. Wilkerson, Mathematics
Faculty Mentors: Dr. Sindhu Unnithan, Mathematics; Dr. V.J. DuRapau, Jr., Mathematics
Abstract
This paper is aimed at introducing hypothesis testing, focusing on the paired t-test. It will
explain how the paired t-test is applied to statistical analyses using an example. Specific
formulas that are used to calculate values based on the data recorded in the example are
given. This paper was originally submitted as part of the required senior Colloquium
presentation for Mathematics majors at Xavier. It is required to research a topic in
mathematics or statistics, and present it to fellow students, faculty, and staff of the
mathematics department.
Key Terms:
Paired t-test; p-value; Student t-test; Hypothesis Testing
Introduction
Statistical analysis involves the calculation of the mean of a set of values in a
sample used for observational study. Statistical analysis can be applied in many fields.
There are now, many methods that are used to perform a statistical analysis. Hypothesis
testing is one method used in statistics. The objective of this paper to explain a form of
hypothesis testing, called the paired t-test.
Hypothesis Testing
Hypothesis testing is used to make an inference about a population that's under
study. The inference is based on the parameter(s) for the statistic, usually the sample
mean and standard deviation. Suppose it is believed that the mean of a population is zero,
the first step in hypothesis testing is to state the null hypothesis (
). The null hypothesis is the assumption that the mean will be equal to
zero. The alternative hypothesis is the assumption that the mean will be either greater
than zero, less than zero, or simply, not equal to zero. When the alternative hypothesis
states that the mean is less than zero, the test is called a left-tailed test. It is right tailed
when
states that the mean is not equal to zero. The second step in hypothesis testing is to
calculate a test statistic. Based on the value of the test statistic, you will find the p-value
from the table of z-distributions, which is based upon the normal distribution known as
the bell curve. Normal distribution is a function expressed as