Null and Alternative Hypotheses: Fresh Take

  • Write a null and alternative hypothesis for a hypothesis test.
  • Decide if a sample statistic provides enough evidence to reject the null hypothesis.
The null hypothesis, [latex]H_{0}[/latex], is what we assume to be true to begin with. This can often be considered the status quo, and as a result, if you cannot accept the null, it requires some action.

  • For proportion, our parameter is population proportion, denoted [latex]p[/latex], therefore our null hypothesis is [latex]H_0: p = \text{null value}[/latex]

The alternative hypothesis, [latex]H_{A}[/latex], is what we consider to be plausible if the null hypothesis is false. This is usually what the researcher is trying to prove.

  • The alternative hypothesis can be:
    • [latex]H_{A}: p>\text{null value}[/latex],
    • [latex]H_{A}: p<\text{null value}[/latex], or
    • [latex]H_{A}: p \neq \text{null value}[/latex].
A medical trial is conducted to test whether or not a new medicine reduces cholesterol by [latex]25\%[/latex]. State the null and alternative hypotheses.