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# Res 342 Week 2 DQ 1.

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Week 2 DQ 1: Why is a t-statistic, as opposed to a z-statistic, used to test small
populations? When would you use a two population test with a large sample size at your
place of employment, in your education, or in politics? Give an example.
A t-statistic is used to test small populations because we rely on the sample standard
deviation. The test statistic is the difference of the sample means divided by its standard error.
The t-statistic is better utilized than the z-statistic because in a larger sample, the standard
deviation usually is not know and we need the standard deviation for smaller samples. If the
population variances are known, we can use the normal distribution. The t-statistic uses the
sample population in its formula where the z-statistic uses the population variances. The z-
statistic is looking at the whole population, which is correct for a large sample. The t-statistic is
looking at the sample, which is correct for a small sample.
A two population test with a large sample size could be used at a place of employment
to compare salaries, benefits, and revenues. The two-sample test could be used to look at
employee output between two workers with the same job. This test could look at why the
outputs are different, if they are. It could vary depending on work environment, location,
motivation, etc. Managers could look at this test to determine how to create efficiency so that
they receive the output they desire. It could also look at the salaries of two employees with the
same job title. This test could look to see why salaries differ. This could be a result of different
experience background, different education background, or who hired the worker. This
information can help employers to determine a salary base for upcoming positions.
A two population test with a large sample size could be used in education to determine
how different methods of teaching effect students. For example, you could test students who
participate in a class completely online and students who have in-classroom instruction. The
test would have the same subject, same amount of information, same tests, same everything.
The test could determine which method was more efficient for the number of students that
participated in the study. This could help Universities determine how to offer classes to make
the students most successful.

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