We have been provided a scenario for a hypothesis test for a population mean. Decide whether the z-test is an appropriate method for conducting the hypothesis test. Assume that the population standard deviation is known in the given case.

A normal probability plot of the sample data shows no outliers and is quite linear. The sample size is $12$.

First, we need to make sure that the z-test procedure is suitable for the given sample size. To use the z-test, we need to take care of the following conditions,

In case the sample size is$\left(n\right)<15$, then the z-test procedure can be used when the variable is very close to being normally distributed or normally distributed.

If the sample size is between$15<\left(n\right)<30$, then the z-test procedure can be used when there is no outlier in the data or the variable is far from being normally distributed.

If the sample size is greater than $30<\left(n\right)$, then the z-test procedure can be used without any limitation.

Here, the given sample size is small. This means, the sample size $\left(n\right)$is $12\left(<30\right)$.

As the variable is very close to being normally distributed or normally distributed.

Hence, the use of the z-test is appropriate.