The null hypothesis is a statement of equality to be tested. The alternative hypothesis is a statement of inequality that is the complement of the null hypothesis.
H_0: μ ≤ 56 H_a: μ > 56 Claim: μ ≤ 56
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A hypothesis test is used to asses a specific claim about a parameter of a population.
Typical Claims About the Parameter
The parameter is equal to a specific value.
The parameter is greater than a specific value.
The parameter is less than a specific value.
There are two parts to a hypothesis test — the null hypothesis and the alternative hypothesis.
The null hypothesis H_0 is a statement of equality to be tested.
The alternative hypothesis H_a is a statement of inequality that is the complement of the null hypothesis.
A claim can be part of the null or alternative hypothesis. With the above facts in mind, let's consider the given statement.
A valet says that no more than 56 cars can be parked in the parking lot at one time.
The valet's claim says that the maximum of cars that can be parked the parking lot is 56 — the parameter of interest here is the maximum. Let's reword this statement without changing the sense of the original sentence.
A valet says that the maximum of cars that can be parked in the parking lot at one time is 56.
Notice the valet's claim is a statement containing equality. Therefore, we can relate the claim with the null hypothesis. Consequently, the alternative hypothesis is the complement.
Null Hypothesis
Alternative Hypothesis
The maximum number of cars to be parked is less than or equal to 56 (claim) H_a:μ ≤ 56
The maximum number of cars to be parked is greater than 56 H_0:μ > 56
