REAL STATISTICS REAL DECISIONS Putting it all together 342 CHAPTER 6 Confidence Intervals The Safe Drinking Water Act, which was passed in 1974, allows the Environmental Protection Agency (EPA) to regulate the levels of contaminants in drinking water. The EPA requires that water utilities give their customers water quality reports annually. These reports include the results of daily water quality monitoring, which is performed to determine whether drinking water is safe for consumption. A water department tests for contaminants at water treatment plants and at customers’ taps. These contaminants include microorganisms, organic chemicals, and inorganic chemicals, such as cyanide. Cyanide’s presence in drinking water is the result of discharges from steel, plastics, and fertilizer factories. For drinking water, the maximum contaminant level of cyanide is 0.2 part per million. As part of your job for your city’s water department, you are preparing a report that includes an analysis of the results shown in the figure at the right. The figure shows the point estimates for the population mean concentration and the 95% confidence intervals for m for cyanide over a three-year period. The data are based on random water samples taken by the city’s three water treatment plants. EXERCISES 1. Interpreting the Results Use the figure to determine whether there has been a change in the mean concentration level of cyanide for each time period. Explain your reasoning. (a) From Year 1 to Year 2 (b) From Year 2 to Year 3 (c) From Year 1 to Year 3 2. What Can You Conclude? Using the results of Exercise 1, what can you conclude about the concentrations of cyanide in the drinking water? 3. What Do You Think? The confidence interval for Year 2 is much larger than that for the other years. What do you think may have caused this larger confidence level? 4. How Can You Improve the Report? What can the water department do to decrease the size of the confidence intervals, regardless of the amount of variance in cyanide levels? 5. How Do You Think They Did It? How do you think the water department constructed the 95% confidence intervals for the population mean concentration of cyanide in the water? Include answers to the questions below in your explanation. (a) What sampling distribution do you think they used? Why? (b) Do you think they used the population standard deviation in calculating the margin of error? Why or why not? If not, what could they have used? 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 Year 3 Year 2 Year Year 1 Mean concentration level (in parts per million) Cyanide
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