Write the null and alternative hypotheses. Identify which is the claim.

A study claim that the mean survival time for certain cancer patients treated immediately with chemotherapy and radiation is 30 months.

*Solution*

The null hypothesis, , is a statement that contain a statement of equality, such as ≤ , = , or ≥. The null hypothesis is that the mean survival time to 32 months, or : µ = 32.

The alternative hypothesis, , is the complement of the null hypothesis. It is a statement that must be true if is false, and it contains a statement of inequality, such as < , ≠ , or >.

The alternative hypothesis is that the mean survival time is not equal to 32 months, or : µ = 32.

Thus, the hypothesis test to be conducted is as follows.

: µ = 32

: µ ≠ 32

The claim is the statement made about the population parameter. It can be either the null or alternative hypothesis, depending on how it is worded. Identify which is the claim for this problem.

The claim for this problem is that the mean survival time for certain cancer patients treated immediately with chemotherapy and radiation is 32 months. This corresponds to the null hypothesis .