Assignment:
Taking air samples at random times during a 2-month period, an environmental group finds the standard deviation of ozone concentration measurements in the vicinity of a chemical plant to be 0.03 parts per million (ppm). The group believes the population of ozone measurements is normally distributed, and they have decided to use the 0.03 ppm figure as a baseline for the variability in the values. They will continue taking air samples, with 12 samples taken at random times during each week. If they find that the standard deviation of observations for any given week is abnormally higher or lower than 0.03 ppm, they will conclude that something unusual is happening at the plant. Given that the group is estimating σ as 0.03, and assuming that they are relying on a 98% confidence interval, how high or low would a weekly standard deviation have to be for them to conclude that unusual events are taking place at the plant?
Provide complete and step by step solution for the question and show calculations and use formulas.