1.4 Other types of alternative hypotheses: Independent samples \(t\)-test
In our discussion of the independent samples \(t\)-test, we have only considered the two-sided hypothesis test:
\[H_0:\mu_1 = \mu_2\;\;\text{versus}\;\;H_1:\mu_1 \neq \mu_2,\]
or equivalently,
\[H_0:\mu_1 - \mu_2 = 0\;\;\text{versus}\;\;H_1:\mu_1 - \mu_2 \neq 0.\]
One-sided tests are also possible. For example,
\[H_0:\mu_1 - \mu_2 = 0\;\;\text{versus}\;\;H_1:\mu_1 - \mu_2 < 0.\]
or
\[H_0:\mu_1 - \mu_2 = 0\;\;\text{versus}\;\;H_1:\mu_1 - \mu_2 > 0.\]
In addition, we can test for differences between groups that are greater, less than, or not equal to a specified value other than 0. For example:
\[H_0:\mu_1 - \mu_2 = 5\;\;\text{versus}\;\;H_1:\mu_1 - \mu_2 \neq 5,\]
or
\[H_0:\mu_1 - \mu_2 = 5\;\;\text{versus}\;\;H_1:\mu_1 - \mu_2 < 5,\]
or
\[H_0:\mu_1 - \mu_2 = 5\;\;\text{versus}\;\;H_1:\mu_1 - \mu_2 > 5.\]
Although we may have a chance to see how these additional types of hypotheses work in the computer lab, you will not be required to use them for the purposes of this subject.