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.
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.
Jack thinks it takes less than 10 minutes to ride his bike from his home to the store.
Notice that Jack's claim is a statement of inequality and it does not include equality. Therefore, we can relate the claim with the alternative hypothesis. Consequently, the null hypothesis is the complement.
Null Hypothesis
Alternative Hypothesis
The mean is greater than or equal to 10 minutes H_0:μ ≥ 10
The mean is less than 10 minutes (claim) H_a:μ < 10
