Question

Suppose that you want to perform a hypothesis test for a population mean, μ.

a. Express the null hypothesis both in words and in symbolic form.

b. Express each of the three possible alternative hypotheses in words and in symbolic form.

Short answer

Part (a).$H_0:\mu ={\mu }_0$

Part (b).

localid="1651760621198" $$\begin{gathered} H_0:\mathit{\mu }={\mu }_0 \\ {H}_a:\mathit{\mu }={\mu }_0 \\ {H}_a:\mathit{\mu }\mathbf{<}{\mu }_0 \end{gathered}$$

Step-by-step solution

Part (a) Step 1. Given information. 

A hypothesis test for given population mean, $\mu$.

Part (a) Step 2. Expression of null hypothesis

According to the null hypothesis, the value of population mean is equal to ${\mu }_0$.

In symbolic form$H_0:\mu ={\mu }_0$.

Part (b) Step 1. Alternate hypotheses

1. The population mean and are equal, according to the alternative hypothesis$\mu$and ${\mu }_0$are equal.

In symbolic form $H_0:\mu ={\mu }_0$

2. The population mean and are different, according to the alternative hypothesis. $\mu$and ${\mu }_0$are greater.

In symbolic form $H_0:\mu >{\mu }_0$

3. The population mean, according to the alternative hypothesis, $\mu$is less than${\mu }_0$is less than

In symbolic form $H_0:\mu <{\mu }_0$