Question

ATATES ONIO NO PUTTING IT ALL TOGETHER Real Statistics — Real Decisions UNITED AVIRONNEMENT PROTECTION Cyanide In 1974, the Safe Drinking Water Act was passed “to protect public health? by regulating the nation's public drinking water supply." In accordance with the act, the Environmental Protection Agency (EPA) has regulations that limit the levels of contaminants in drinking water supplied by water utilities. These utilities are required to supply water quality reports to their customers annually. These reports discuss the source of the water, its treatment, and the results of water quality monitoring that is performed daily. The results of this monitoring indicate whether or not drinking water is healthy enough for consumption A water department tests for contaminants at water treatment plants and at customers' taps. These regulated parameters include microorganisms, organic chemicals, and inorganic chemicals. For instance, cyanide is an inorganic chemical that is regulated. Its presence in drinking water is the result of discharges from steel, plastics, and fertilizer factories. The maximum contaminant level for cyanide is set at 0.2 part per million. You work for a city's water department and are interpreting the results shown in the graph at the right. The graph shows the point estimates for the population mean concentration and the 95% confidence intervals for for cyanide over a three-year period. The data are based on random water samples taken by the city's three water treatment plants Mean concentration level a parts per million) 012 011 0.10 0.09 0.08 0.07 Dos 0.05 0.04 003 0.02 0.01 Yout Your 2 Year Year 3

Answer 1

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1: There has been change in mean concentration level of Cyanide from Year 1 to Year 2 and Year 1 to Year 3 since their confidence interval is not overlapping. The Year 2 to Year 3 confidence interval is overlapping and hence the change is not significant.

2. We conclude that as from Year 1 to Year 2 or 3, the mean level of concentration of cyanide has increased. There has been no significant change from Year 2 to Year 3.

3. Since this is the year where the concentration increases, it may be the case that many observations were found out to be low and many were high leading to the higher variance in the observed sample. Since, higher variance sees a larger confidence interval, we expect to see larger interval. In Year 3, the concentration stabilizes and variance goes down again.

4. They have used the normal distribution as sampling distribution and to since variance is unknown, they would have used t-distribution.

They did not use population standard deviation as we can see the interval is much wider for year two which indicates that the variance must be higher for the sample in Year 2 which indicates that the variance and standard deviation is being estimated from the sample.