High concentration of the toxic element arsenic is all too common in groundwater. The article “Evaluation of Treatment Systems for the Removal of Arsenic from Groundwater”

(Practice Periodical of Hazardous, Toxic, and Radioactive Waste Mgmt., 2005: 152–157) reported that for a sample of n
5 water specimens selected for treatment by coagulation, the sample mean arsenic concentration was 24.3 g/L, and the sample standard deviation was 4.1. The authors of the cited article used t-based methods to analyze their data, so hopefully had reason to believe that the distribution of arsenic concentration was normal.

a. Calculate and interpret a 95% CI for true average arsenic concentration in all such water specimens.

b. Calculate a 90% upper confidence bound for the standard deviation of the arsenic concentration distribution.

c. Predict the arsenic concentration for a single water specimen in a way that conveys information about precision and reliability.