📊AP Statistics
4. A state environmental protection agency is investigating the water quality of a major river system. Specifically, the agency is measuring dissolved oxygen (DO) levels, in milligrams per liter (mg/L). Healthy aquatic ecosystems typically require DO levels above 5.0 mg/L. The agency wants to determine if a newly constructed industrial plant is negatively impacting the DO levels downstream compared to the upstream levels.
Region | n | Mean | Standard Deviation | Minimum | Q1 | Median | Q3 | Maximum |
|---|---|---|---|---|---|---|---|---|
Downstream | 60 | 5.3 | 1.1 | 3.2 | 4.8 | 5.4 | 6.1 | 8.5 |
Upstream | 60 | 7.2 | 0.8 | 5.1 | 6.7 | 7.3 | 7.8 | 9.0 |
The agency initially considers collecting 60 water samples by taking one sample at noon each day for two months from a single, easily accessible public dock located just downstream of the plant. Identify a potential source of bias in this sampling method and explain how this bias would likely affect the estimate of the mean dissolved oxygen level for all downstream water.
The agency ultimately decides against the method in Part A. Instead, they select a simple random sample of 60 locations downstream of the plant and a separate simple random sample of 60 locations upstream of the plant, collecting one water sample from each location. The summary statistics for the dissolved oxygen levels (in mg/L) are shown in Table 1. Using the data in Table 1, determine whether the maximum downstream DO level of 8.5 mg/L is considered an outlier using the rule. Show your work.
A specific downstream location from the sample has a DO level of 4.1 mg/L. A specific upstream location from the sample has a DO level of 5.5 mg/L. Using the data in Table 1, calculate the standardized score (z-score) for each of these two locations relative to their respective regions. Which location has a dissolved oxygen level that is relatively lower compared to its own region?
The agency will mandate environmental interventions for the industrial plant if two conditions are met: (1) the data collection method allows for generalization to the entire river system (both upstream and downstream), and (2) there is statistical evidence that downstream DO levels are generally lower than upstream DO levels. Based on the study design described in Part B and the summary statistics in Table 1, should the agency mandate the interventions? Justify your conclusion using evidence for both conditions.
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