When the alternative hypothesis is non-directional, we use a two-tailed test.
Example:
H0: mean = 50
Ha : mean not equal to 50
Here is a directional hypothesis that would use a one-tailed test.
H0: mean = 40
Ha : mean > 40
or
H0: mean = 40
Ha: mean < 40
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You use a z test when you are testing a hypothesis that is using proportions You use a t test when you are testing a hypothesis that is using means
The choice of one-tailed or two-tailed tests follows the logic of the hypothesis that is being tested! The one-tailed test, if appropriate, will be more powerful.
It depends on the population.Use t-test for a small population, N < 30; otherwiase, apply z-test or when N>=30.
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They are used to test hypothesis such as the mean is some value where you do not know if otherwise the mean is less or more.