Chapter 15, Problem 15.102ACA

Groundwater contamination of wells. Methyl tert-butyl ether (MTBE) is a lead fuel additive that can contaminate drinking water through leaking underground storage tanks at gasoline stations. A study published in Environmental Science & Technology (January 2005) investigated the risk of exposure to MTBE through drinking water in New Hampshire. Data were collected for a sample of 223 public and private New Hampshire wells and are saved in the MTBE file.

1. a. Suppose environmental regulations stipulate that only half the wells in the state should have MTBE levels that exceed .5 microgram per liter. Do the data collected by the researchers provide evidence to indicate that the median level of MTBE in New Hampshire groundwater wells is less than .5 microgram per liter? (The MTBE level is recorded in the variable named MTBE.) Yes.
2. b. One of the objectives of the study was to determine if the level of MTBE contamination is different for private and public wells and for bedrock and unconsolidated aquifers For this objective, the researchers focused on 70 sampled wells that had detectable levels of MTBE. (These wells are identified on the data set as “Detect” in the DETECTION variable.) Specifically, they wanted to determine if the distribution of MTBE levels in public wells is shifted above or below the distribution of MTBE levels in private wells and if the distribution of MTBE levels in bedrock aquifers is shifted above or below the distribution of MTBE levels in unconsolidated aquifers. Conduct the appropriate analysis to answer these questions. (The variable WELLCLASS identifies public and private wells. The variable AQUIFER identifies bedrock and unconsolidated aquifers.)
3. c. The environmental researchers also investigated how the combination of well class and aquifer affected the MTBE levels of the wells. Although there are four possible combinations of well class and aquifer, there were data available for only three: Private/bedrock, Public/bedrock, and Public/unconsolidated. (These three levels are identified in the COMBINE variable on the data set.) Compare the distributions of MTBE levels for these three groups of wells. Interpret the results for the researchers. Explain why your choice of α for this analysis is critical.
4. d. The researchers also wanted an estimate of the correlation between the MTBE level of a groundwater well and the depth (in feet) of a well. (The depth of the well is recorded in the DEPTH variable on the data set.) Because MTBE level is not normally distributed, they used Spearman s rank correlation method. Also, because earlier analyses indicated that public and private wells have different MTBE distributions, the rank correlation was computed separately for each well class. Conduct the analysis for the researchers. Interpret the results, practically.