Chapter 9, Problem 1CR

(a) List the steps in testing a hypothesis, (b) Why can't a hypothesis ever be proven?

To determine

List the steps in testing a hypothesis.

Explanation of Solution

Steps in testing a hypothesis:

Step 1: Identify the claim and state the null and alternative hypotheses.

Step 2: Specify the decision rule. That is, identify the level of significance, critical values and rejection regions.

Step 3: Obtain the test statistic value.

Step 4: Make decisions about deciding whether to reject or fail to reject the null hypothesis

Step 5: Interpret the decision.

To determine

Explain why a hypothesis cannot ever be proven.

Explanation of Solution

The decisions that can be made by performing a hypothesis test are as follows:

• Reject $H_0$
• Fail to reject $H_0$.

The above decision indicates that,

• If the null hypothesis is rejected, then the conclusion is that there is enough evidence to reject $H_0$.
• If the null hypothesis is not rejected, then the conclusion is that there is no enough evidence to reject or fail to reject $H_0$.

From the decision, the hypothesis cannot ever be proven because,

• The hypothesis will be fair today, but it could be disproved tomorrow for new data.
• The hypothesis might be tested repeatedly when the null hypothesis is not rejected.