€¢(1) Explain when to use a t-test and when to use a
z-test. Explore the differences.

€¢(2)
Discuss why samples are used instead of populations.

(1)

The
z- test and t- test are basically the same; they compare two means to suggest
whether the two samples come from the same population. These tests can also be used to examine
whether the mean has a specified value. There are variations in the t- test.
If you have a sample and wish to compare it with a known mean the single
sample t- test is available. If your samples are not independent of each
other and have some factor in common, i.e. geographical location or before/after
treatment, the paired sample t- test can be applied. There are also two
variations on the two sample t- test, the first uses samples that do not have
equal variances and the second uses samples whose variances are equal.

A
z- test is applicable if the data satisfies the following conditions:

(a)
The data points should be independent of each other

(b)
The sample size, n