# Alternative Hypothesis

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Definition

In a test of hypothesis, the alternative hypothesis is a statement about one or more process/population distributions that is accepted if the null hypothesis is rejected. The null and alternative hypotheses are mutually exclusive (if one is true, the other must be false) and together, they cover the entire parameter space (all possible scenarios) under consideration.

Examples

Consider the null hypothesis H0: The process mean is equal to the historical value (µ = µ0)

If the set of possible values for the process mean (parameter space) includes values that are less than, greater than or equal to the historical mean, then the alternative hypothesis is H1: The process mean differs from the historical value (µ ≠ µ0)

If the parameter space only includes values that are less than or equal to the historical mean, then the alternative hypothesis is H1: The process mean is greater than the historical value.

Application

The alternative hypothesis is the claim we wish to establish, by rejecting the null. Therefore, the null is usually a statement of no effect whereas the alternative states the effect of interest.