Suppose employees and customers of bank x were exposed to a gas pipe leak containing a hazardous substance that passes 6 metres below bank x in a shopping mall at Mpumalanga Province. All individuals

Question

Suppose employees and customers of bank x were exposed to a gas pipe leak containing a hazardous substance that passes 6 metres below bank x in a shopping mall at Mpumalanga Province. All individuals inside the vicinity of Bank x were exposed to this chemical and were tested for the level of contamination. The following figures are the hours spent in the affected area since the leak and the contamination levels (in parts per million) of the first ten individuals who entered Bank x before it was discovered that there was a leak after an unexpected explosion at the industrial area where Bank X is situated. After the leak was discovered, all individuals were put in a separate area to minimize the chemical gas contamination from the public.
	able[[Minutes spend, 3, 3, 4, 5, 6, 6, 8, 8, 10, 11], [Contamination level, 25, 28, 27, 39, 46, 48, 61, 58, 75, 82]]
Search And Select
(a) Enter the data in Excel using the first two columns and put labels and attach the spreadsheet.
(2)
(b) Determine the independent and dependent variables.
(2)
(c) Plot the scatter diagram and ensure that you put the labels and title of the graph.
Comment on the relationship from the scatter diagram.
(4)
(d) Use

VIPSolutions · Accepted Answer

# Bank X Chemical Leak Data Analysis

## (a) Entering Data in Excel

**Table: Minutes Spent and Contamination Levels**

| Minutes Spent | Contamination Level (ppm) |
|:-------------:|:------------------------:|
| 3             | 25                       |
| 3             | 28                       |
| 4             | 27                       |
| 5             | 39                       |
| 6             | 46                       |
| 6             | 48                       |
| 8             | 61                       |
| 8             | 58                       |
| 10            | 75                       |
| 11            | 82                       |

- **Column A:** Minutes Spent (label cell A1)
- **Column B:** Contamination Level (ppm) (label cell B1)

_**[Attach your .xlsx spreadsheet file here if required by your assignment platform.]**_

---

## (b) Independent and Dependent Variables

- **Independent Variable:** Minutes Spent (since this is what you control or observe before measuring contamination)
- **Dependent Variable:** Contamination Level (ppm) (since this depends on time spent)

---

## (c) Scatter Diagram and Interpretation

**How to Plot in Excel:**
1. Highlight both columns (including labels).
2. Go to `Insert` → `Chart` → `Scatter (X, Y)` → `Scatter with only Markers`.
3. Add axis titles:  
   - X-axis: Minutes Spent  
   - Y-axis: Contamination Level (ppm)
4. Add a chart title, e.g., "Contamination Level vs. Minutes Spent in Bank X".

**Scatterplot Relationship:**
- The scatter diagram will show an upward trend, indicating a positive relationship: **the longer someone stays, the higher their contamination level**.

---

## (d) Excel Formula for Slope

Use the formula:
```excel
=SLOPE(B2:B11, A2:A11)
```
Replace B2:B11 with your contamination data range, and A2:A11 with your minutes data range.

---

## (e) Excel Formula for Intercept

Use the formula:
```excel
=INTERCEPT(B2:B11, A2:A11)
```

---

## (f) Regression Line

The regression line has the form:
$$
\text{Contamination Level} = \text{Intercept} + (\text{Slope} \times \text{Minutes Spent})
$$

If, for example, Slope = 6 and Intercept = 8 (plug in your calculated values):

$$
\text{Contamination Level} = 8 + 6 \times (\text{Minutes Spent})
$$

---

## (g) Excel Formulas for Coefficient of Determination and Correlation

- **Coefficient of Determination ($R^2$):**
    ```excel
    =RSQ(B2:B11, A2:A11)
    ```
- **Coefficient of Correlation ($r$):**
    ```excel
    =CORREL(A2:A11, B2:B11)
    ```

---

## (h) Interpretation of Coefficients

- **Coefficient of Determination ($R^2$)**: Measures the proportion of variance in contamination level explained by minutes spent. If $R^2 = 0.95$, then 95% of the contamination variation is explained by time spent.
- **Coefficient of Correlation ($r$)**: Shows the strength and direction of the linear relationship. If $r = 0.97$, there is a strong positive linear relationship.

---

## (i) Estimating Contamination Level

**Regression formula:**
$$
\text{Contamination Level} = \text{Intercept} + \text{Slope} \times \text{Minutes}
$$

**For 13 minutes:**
$$
\text{Contamination Level}_{13} = \text{Intercept} + \text{Slope} \times 13
$$

**For 30 minutes (fatal exposure):**
$$
\text{Contamination Level}_{30} = \text{Intercept} + \text{Slope} \times 30
$$

**Plug in your calculated slope/intercept from steps (d) and (e).**

---

## Recommendations About the Chemical Pipe

- **Immediate Action:** Relocate or reinforce the chemical pipe to prevent future leaks, especially in public and commercial spaces.
- **Monitoring:** Install continuous gas detection and alarm systems in the mall/bank vicinity.
- **Regulatory Compliance:** Ensure the pipe meets all safety and maintenance standards; conduct regular inspections.
- **Emergency Preparedness:** Develop and practice evacuation and containment procedures for similar incidents.
- **Public Health:** Provide medical monitoring and long-term health support for exposed individuals.

---

**Note:** Replace example numbers with your calculated values from Excel.  
**Alt text for scatterplot:** "Scatterplot showing a positive linear relationship between minutes spent in Bank X and contamination level (ppm)."

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