For any sample that comes from a normally distributed population, we know that:
$(\bar{x} - \mu)/(\sigma/\sqrt{n}) \sim N(0,1)$ when $\sigma$ is known

Thus, a 95% CI for the mean, $\mu = \bar{x} \pm z_{\alpha/2} \times \frac{\sigma}{\sqrt{n}}$ where $\alpha = 0.05$
$= \text{USD } 72,000 \pm 1.96 \times \text{USD } \frac{7,800}{\sqrt{120}}$
$= \text{USD } 72,000 \pm \text{USD } 1,395.60$
Which can be expressed as (USD 70,604.40, USD 73,395.60).

Section: Quantitative Analysis
Chapter: Hypothesis Testing
Learning objectives:

• Differentiate between a one-sided and a two-sided test and identify when to use each test.
• Construct and apply confidence intervals for one-sided and two-sided hypothesis tests and interpret the results.