The Four Parts Of a Hypothesis Test



The Four Parts Of a Hypothesis Test Summary

I. All hypothesis tests begins with an "assumption", called the null hypothesis. It is an assumption about the value a population parameter. For example, “the true mean µ of the population is 5”). The null hypothesis ALWAYS involves an “equal” sign in its statement e.g., µ = 5). Again …. it is only an assumption and may later be “rejected” based upon information provided by sample observations taken from the population.

II. The alternative hypothesis is a statement about the population parameter that opposes the equality statement in the null hypothesis. The statement opposing equality in the null hypothesis will always be one of the inequalities “>” or “ 5 or µ < 5 or µ ≠ 5.

III. A sample is taken from the population and a certain numerical value is calculated using the null hypothesis and the sample taken from the population. This numerical value is called the test statistic and is used in IV. below.

IV. The rejection region may be viewed as the set of possible values of the test statistic that has a low probability of occurrence when the null hypothesis is true. This low probability of occurrence is called the significance level of the test and is denoted by α. While there are infinitely many possible choices, the values of α will be limited to .1, .05 and .01.

The null hypothesis, alternative hypothesis and significance level of the test completely determine the rejection region.

If the calculated test statistic is within in the rejection region we conclude that the null hypothesis (assumption) was flawed since there is a low probability, α, of this happening. Therefore, we reject the null hypothesis, and accept, as an alternative, the alternative hypothesis.

Note: Since the null hypothesis an assumption, we can never accept the null hypothesis. The best we can do is to determine if the test statistic, based upon a sample from the population “disagrees” with the assumed null hypothesis. If we cannot reject the null hypothesis at a selected significance level, there is insufficient information (in the sample and at that significance level) to draw any conclusion whatsoever about validity or invalidity of the null hypothesis.

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