pH Level Variations in Freshwater Lake

Question

pH level Acid rain
Day 1 7.5 0
Day 2 6.75 0
Day 3 5.25 14 mm
Day 4 5.0 37 mm
Day 5 6.25 0
Day 6 11.0 0
Day 7 7.2 0
Day 8 6.5 0
Day 9 5.25 12 mm
Day 10 5.0 32 mm
Day 12 5.1 16 mm
Day 14 6.5 0
We can see that the pH level fluctuated between 5.0 to 11.0 and that acid rain fell only on days 3, 4, 9, 10, and 12.

Step 2: Consider Visual Representations
To understand this data better, it may be helpful to graph it. First, think about what type of graph makes the most sense for this data set and why.

Step 3: Graph the Data
Now, it’s your turn to evaluate the data using visualizations. In a word processing document, spreadsheet document, or on poster board, create a graph of the data.

Step 4: Look for Statistical Features, Patterns, Sources of Error, and Limitations
As you look at your graph, analyze the data by identifying and explaining statistical features like the shape of your graph and any patterns, sources of error, or limitations.

Step 5: Set Up and Solve a Math Problem
Look at Days 9, 10, and 12. Imagine you are asked to determine if there is a specific mathematic relationship between the amount of acid rain and the pH level. Take notes on how you would test this idea:

What methods would be efficient and appropriate to use? Why?
How could you adopt these methods/procedures to try this idea out on other days in the data chart?
Explain to a classmate what your plan to solve this would be. Use the classmate’s feedback to improve your efficiency in solving.
What can you determine based on the methods you have chosen? Is there a specific mathematic relationship between the amount of acid rain and the pH level? Explain.
Step 6: What to Submit
To complete this activity, submit the following:

Your graph (Step 3)
Explanations of shape, patterns, sources of error, or limitations (Step 4)
Your answers (Step 5)

Answer 1

Step 3: Graph the Data

To visualize the variations of pH levels in the freshwater lake alongside the amount of acid rain, a line graph is the most appropriate. The X-axis will represent the Days (from Day 1 to Day 14), and the Y-axis will represent the pH level. A secondary Y-axis can be used to represent the amount of acid rain in mm if desired, but a simpler approach is to include a bar graph overlay of acid rain on the same graph. Below is a simplified illustration of the graph you could create.

(Visual representation: Create a line graph with pH levels represented by a line and acid rain represented by bars)

Step 4: Analysis of the Graph

Statistical Features:

• Shape:
  • The pH levels exhibit significant fluctuation, especially on days when acid rain occurred. The pH dropped sharply on Days 3 and 4, correlating with the acid rain.
  • There is a notable spike in the pH level on Day 6 (11.0), which stands out as an outlier.

Patterns:

• The data suggests a negative correlation between acid rain and pH level, particularly on days with recorded acid rain.
• The lowest pH values (5.0 to 5.25) coincided with days that had significant acid rain (Day 4 with 37 mm and Day 10 with 32 mm).

Sources of Error:

• Possible external factors not accounted for, such as other pollutants, temperature fluctuations, or freshwater inflow from other sources that might influence pH levels.
• Measurement errors in either the pH readings or the acid rain amounts.

Limitations:

• The dataset only spans 14 days, which may not reflect long-term trends or seasonal variations.
• The pH readings on Days 5, 6, 7, and 14 may not accurately reflect the effect of acid rain as no acid rain occurred on those days.

Step 5: Math Problem Setup

Hypothesis:

Determine if there is a mathematical relationship between the amount of acid rain and the pH level of the freshwater lake.

Methods to Test:

1. Data Analysis:

   • Use correlation coefficients (Pearson’s correlation) to quantify the relationship between acid rain and pH levels specifically on Days 9, 10, and 12.
   • Create a scatter plot with acid rain on the X-axis and pH levels on the Y-axis to visually assess the relationship.

2. Regression Analysis:

   • Conduct a linear regression analysis to determine if there's a predictive relationship between acid rain amounts and pH values.

3. Adopting Methods for Other Days:

   • Expand the analysis by selecting other days with varying acid rain amounts and pH readings to test the relationship.
   • Compile data into a larger spreadsheet for comprehensive statistical analysis.

Explanation to a Classmate:

“Alright! To find out whether there's a specific relationship between acid rain and pH levels, I'm going to analyze Days 9, 10, and 12. First, I'll calculate the correlation coefficient to see how closely related the two variables are. If I find a strong correlation, I'll use linear regression to see if we can predict pH levels based on acid rain amounts. After that, I can apply these methods to the rest of the data to see if the pattern holds across other days.”

Determining Relationship:

Based on the methods chosen:

• If a significant correlation coefficient (close to -1) results, we could conclude a strong inverse relationship where increased acid rain leads to lower pH levels.
• The scatter plot would likely show a downward trend if a relationship does exist.

Step 6: Submission

This is the complete document that you can submit containing:

1. The graph (illustration for Step 3).
2. Explanations regarding statistical features, patterns, sources of error, and limitations (Step 4).
3. Your analysis and methodology for testing the relationship between acid rain and pH levels (Step 5).