The Environmental Protection Agency (EPA) has determined that safe drinking water should contain at most 1.3 mg/liter of copper, on average. A water supply company is testing water from a new source and collects water in small bottles at each of 30 randomly selected locations. The company performs a test at the α=0.05 significance level of H₀: μ = 1.3 versus H_a: μ > 1.3, where μ is the true mean copper content of the water from the new source.

a. Describe a Type I error and a Type II error in this setting.

b. Which type of error is more serious in this case? Justify your answer.

c. Based on your answer to part (b), do you agree with the company’s choice of α = 0.05? Why or why not?