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The report "Testing the Waters \(2009^{\prime \prime}\) (www nrdcorg) included information on the water quality at the 82 most popular swimming beaches in California. Thirty-eight of these beaches are in Los Angeles County. For each beach, water quality was tested weekly and the data below are the percent of the tests in 2008 that failed to meet water quality standards. Los Angeles County \(\begin{array}{llllllllll}32 & 4 & 6 & 4 & 4 & 7 & 4 & 27 & 19 & 23\end{array}\) \(\begin{array}{lll}7 & 4 & 27\end{array}\) \(\begin{array}{rrrr}6 & 4 & 4 & 7 \\\ 11 & 19 & 9 & 11\end{array}\) \(\begin{array}{rr}32 & 4 \\ 19 & 13\end{array}\) \(\begin{array}{llllllllll}19 & 13 & 11 & 19 & 9 & 11 & 16 & 23 & 19 & 16\end{array}\) \(\begin{array}{llllllllll}33 & 12 & 29 & 3 & 11 & 6 & 22 & 18 & 31 & 43\end{array}\) \(\begin{array}{llllllll}17 & 26 & 17 & 20 & 10 & 6 & 14 & 11\end{array}\) Other Counties 0 0 0 \(2 \quad 3\) 7 511 \(5 \quad 7\) \(\begin{array}{lllllll}15 & 8 & 1 & 5 & 0 & 5 & 4\end{array}\) 1 0 0 5 \(\begin{array}{lllllll}1 & 0 & 2 & 7 & 0 & 2 & 2\end{array}\) 3 3 \(\begin{array}{lllllllll}0 & 8 & 8 & 8 & 0 & 0 & 17 & 4 & 3\end{array}\) : \(\begin{array}{lll}10 & 40 & 3\end{array}\) a. Construct a dotplot of the percent of tests failing to meet water quality standards for the Los Angeles County beaches. Write a few sentences describing any interesting features of the dotplot. b. Construct a dotplot of the percent of tests failing to meet water quality standards for the beaches in other counties. Write a few sentences describing any interesting features of the dotplot. c. Based on the two dotplots from Parts (a) and (b), describe how the percent of tests that fail to meet water quality standards for beaches in Los Angeles county differs from those of other counties.

Step by step solution

01

Construction of Dotplot for Los Angeles county

- Arrange the water quality failure results in ascending order.\n- Draw a horizontal axis, and mark it with reasonable scale considering the given data.\n- For each given failure rate, place a dot in a corresponding position on the scale. If multiple beaches have the same failure rate, you stack the dots vertically.

02

Construction of Dotplot for Other Counties

This step is fundamentally identical to step 1, except it's applied to the data from the other counties:\n- The data of the other counties should be arranged in ascending order.\n- A horizontal axis should be drawn for this data.\n- Placement of dots on this new plot follows the same procedure as in Step 1.

03

Interpretation and Comparison

Interpret and compare the two plots:\n- Look for the mode, median, and spread of the data in both plots.\n- Compare the water quality in Los Angeles County to that in other counties based on these statistical measures.\n- Look for any significant features or outliers and compare them in both cases.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Water Quality Standards

Water quality standards are crucial guidelines that determine the safety and cleanliness of natural water bodies like oceans, lakes, and rivers. These standards help identify how much pollution is acceptable for water to be considered safe for human contact.
The standards are usually set by environmental protection agencies and aim to protect public health, maintain environmental integrity, and ensure clean drinking water sources.
Testing water quality often involves measuring different pollutants, such as bacteria, nitrogen, or heavy metals, and checking if these concentrations exceed established safe levels.

• If the concentration of a contaminant in the water exceeds the threshold set by the standards, this means the water is unsafe for activities like swimming.
• Using these standards helps to assess and compare different bodies of water, ensuring communities are informed about potential health risks.

In the context of the exercise, the water quality standards were used to test beaches based on the percentage of tests that failed in 2008. This data helps in understanding how well a beach complies with safety standards.

Los Angeles County Beaches

Los Angeles County beaches are popular destinations for recreation and relaxation. Hence, maintaining high water quality is essential for public health and tourism.
The exercise provides data on the percentage of water quality tests that failed across various beaches in Los Angeles County. These percentages give insights into how frequently the water did not meet safety standards.
Think of each percentage as an indicator of how clean each beach is, helping people decide where it's safe to swim. For example, a beach with a higher percentage of test failures might suggest that the water is more polluted compared to one with a lower percentage.

• The dotplot constructed using this data helps visualize which beaches had higher failure rates, indicating a recurring issue with certain areas.
• This form of visualization makes it easier to spot trends, such as beaches that consistently show poor water quality.

The data from these beaches provides invaluable information for local authorities to take necessary actions like issuing warnings or implementing cleanup efforts.

Data Interpretation

Data interpretation involves analyzing information (such as those from environmental tests) to derive meaningful insights and conclusions. In this exercise, the objective is to interpret percentages of failed water quality tests from Los Angeles County and compare them against other counties.
The dotplot is an essential tool for data interpretation. It helps by visually representing the frequency of data points, which, in this case, shows how often certain failure rates occur across multiple beaches.

• When interpreting the dotplot, focus on identifying patterns such as clustering of data points, which could indicate common failure rates.
• Outliers are also important as they represent extreme values that might require special attention.

Comparing dotplots from Los Angeles County and other counties reveals differences and similarities.
This comparison helps to understand whether Los Angeles County's beaches generally have better or worse water quality than those in other areas, guiding policymakers and environmentalists in targeting specific problems for improving water conditions.