Question

Suppose that you are considering a hypothesis test for a population mean, u. In each part, express the alternative hypothesis symbolically and identify the hypothesis test as two tailed, left tailed, or right tailed.

a. You want to decide whether the population mean is different from a specified value ${\mu }_0$.

b. You want to decide whether the population mean is less than a specified value ${\mu }_0$.

c. You want to decide whether the population mean is greater than a specified value to ${\mu }_0$.

Short answer

Part (a). This hypothesis is a two-tailed test.

Part (b) This hypothesis is a left-tailed test.

Part (c) This hypothesis is a right-tailed test.

Step-by-step solution

Part (a) Step 1. Given information. 

Considering a hypothesis test for a population mean, $\mu$.

Part (a) Step 2. Alternative hypothesis

The alternative hypothesis can be symbolized as follows:

$H_a:\mu \ne {\mu }_0$

This hypothesis is a two-tailed test.

Part (b) Step 1. Alternative hypothesis 

Symbolically, the alternative hypothesis is:

$H_a:\mu <{\mu }_0$

This hypothesis is a left-tailed test.

Part (c) Step 1. Alternative hypothesis 

The Alternative hypothesis can be expressed symbolically,

$H_a:\mu >{\mu }_0$

This hypothesis is a right-tailed test.