A field team measures the nitrate concentration in water samples from a catchment. The eight samples are selected independently at random. Assume that the population of nitrate concentrations is normally distributed, with known standard deviation $1.2\text{ mg L}^{-1}$

Figure 1 shows the measured concentrations. The team will test whether the population mean concentration exceeds $5.0\text{ mg L}^{-1}$ using

$$H_0:\mu=5.0,\qquad H_1:\mu>5.0,$$

where $\mu$ is measured in $\text{mg L}^{-1}$