Question

There are three possible alternative hypothesis in a hypothesis test for population mean. Identify them, and explain when each is used.

Short answer

\(H_{a}:\mu \neq \mu ^{_{0}}, H_{a}:\mu >\mu _{0}\) and \(H_{a}:\mu < \mu ^{_{0}}\)

Step-by-step solution

Step 1. Types of hypothesis

The choice of the alternative hypothesis depends on and should reflect the purpose of the hypothesis test. Three choices are possible for the alternative hypothesis.

• Two-tailed test
• Left-tailed test
• Right-tailed test

Step 2. Explanation

The given information states that there are three possible alternative hypothesis in a hypothesis test for a population mean are as shown below:

The population mean differs from the specified value \(\mu _{0}:\)

\(H_{a}:\mu \neq \mu ^{_{0}} \)

The population mean is greater than the specified value \(\mu _{0}:\)

\(H_{a}:\mu >\mu _{0}\)

The population mean is less than the specified value \(\mu _{0}:\)

\(H_{a}:\mu < \mu ^{_{0}}\)

Thus, the three possible alternative hypothesis are \(H_{a}:\mu \neq \mu ^{_{0}}, H_{a}:\mu >\mu _{0}\) and \(H_{a}:\mu < \mu ^{_{0}}\).