Null and Alternative Hypothesis for Means: Fresh Take

  • Explain the purpose of hypothesis testing.
  • Write the null and alternative hypotheses for tests on population means.
  • Check the conditions for hypothesis tests for population means.
The null hypothesis ([latex]H_0[/latex]) is a statement of no change or status quo. Symbol used for the null hypothesis is [latex]=[/latex].

The alternative hypothesis ([latex]H_A[/latex]) is sometimes referred to as the research hypothesis; it is what the researcher believes to be true based on the data to be collected. Symbols used for the alternative hypothesis are [latex]\lt[/latex], [latex]\gt[/latex], and [latex]\ne[/latex].

We want to test whether the mean GPA of students in American colleges is different from 2.0. The null and alternative hypotheses are:

[latex]H_0: \mu=2.0[/latex][latex]H_A: \mu \ne 2.0[/latex]

Note: Because we are testing [latex]\ne[/latex], this is a two-tailed test.