Question 1: A major manufacturing firm producing PCB for electrical insulation discharges small amounts from the plant. We assume that the amount of PCB discharge per water specimen is normally distributed with known standard deviation . Production will be halted if there is evidence that the mean PCB amount discharged in the water exceeds 3 ppm (parts per million). A random sample of 16 water specimens produced ppm.

a) Do these statistics provide sufficient evidence to halt the process? Use .

b) Briefly discuss the consequences of type I and type II errors. From your point of view, which of the two errors is the most serious?

c) Construct a 99% confidence interval for the true mean PCB amount discharged in the water.