Question

Regarding a hypothesis test:

a. What is the reason, generally, for deciding whether the null hypothesis should be rejected.

b. How can the procedure identified in part (a) be made objective and precise?

Short answer

a). Take a random sample from the population. If the sample data are consistent with the null hypothesis, do not reject the null hypothesis; if the sample data are inconsistent with the null hypothesis (in the direction of alternative hypothesis), reject the null hypothesis and conclude that alternative hypothesis is true.

b). In practice, we establish a precise criterion for deciding whether to reject the null hypothesis prior to obtaining the data.

Step-by-step solution

Step 1. Explanation (a).

To find this, the procedure for declaring is as follows:

Take a random sample from the population. If the sample data are consistent with the null hypothesis, do not reject the null hypothesis; if the sample data are inconsistent with the null hypothesis (in the direction of alternative hypothesis), reject the null hypothesis and conclude that alternative hypothesis is true.

Step 2. Explanation (b).

In practice, we establish a precise criterion for deciding whether to reject the null hypothesis prior to obtaining the data.