For a random sample of size $n$ taken from a random variable $X∼N(\mu, \sigma^2)$, the sample mean ($\bar{X}$) is normally distributed with $\bar{X}∼N\bigg(\mu, \dfrac{\sigma^2}{n}\bigg)$.

To perform the test:

- Define the test statistic
- Determine whether a one-tailed or two-tailed test is needed
- Identify the null and alternate hypotheses accordingly
- Calculate $P(\bar{X} < \bar{x})$ and/or $P(\bar{X} > \bar{x})$
- Compare with the significance level of the test (usually $5\%$) and decide whether or not to reject the null hypothesis
- Conclude with a statement in context of the question