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