Null and Alternative Hypothesis for Means: Apply It 2

  • 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 actual hypothesis test begins by considering two hypotheses. They are called the null hypothesis and the alternative hypothesis. These hypotheses contain opposing viewpoints.

The null hypothesis ([latex]H_0[/latex]) is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt.

  • Null hypothesis: [latex]H_0: \mu_1=\mu_2[/latex] or [latex]H_0: \mu_1-\mu_2=0[/latex]

The alternative hypothesis ([latex]H_A[/latex]) is a claim about the population that is contradictory to [latex]H_0[/latex] and what we conclude when we reject [latex]H_0[/latex].

  • Alternative hypothesis:
    • [latex]H_A: \mu_1\lt \mu_2[/latex] or [latex]H_A: \mu_1-\mu_2\lt 0[/latex]
    • [latex]H_A: \mu_1>\mu_2[/latex] or [latex]H_A: \mu_1-\mu_2>0[/latex]
    • [latex]H_A: \mu_1\ne \mu_2[/latex] or [latex]H_A: \mu_1-\mu_2\ne0[/latex]

Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.