(Round to three decimal places as needed.) (c) Does a linear relation exist between the number of reported cases of Lyme disease and the number of drowning deaths? The variables Lyme disease and drowning deaths are V associated because r is v and the absolute value of the correlation coefficient is than the critical value, (Round to three decimal places as needed.)

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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Only Question C Please

**Data on Lyme Disease Cases and Drowning Deaths**

The table displays monthly data on the number of Lyme Disease cases and drowning deaths:

| Cases of Lyme Disease | Drowning Deaths | Month |
|-----------------------|-----------------|-------|
| 2                     | 0               | J     |
| 2                     | 1               | F     |
| 3                     | 2               | M     |
| 4                     | 1               | A     |
| 5                     | 2               | M     |
| 15                    | 9               | J     |
| 22                    | 17              | J     |
| 13                    | 5               | A     |
| 6                     | 3               | S     |
| 5                     | 3               | O     |
| 4                     | 1               | N     |
| 1                     | 0               | D     |

**Critical Values for Correlation Coefficient**

The table to the right provides the critical values for correlation coefficients based on sample size \(n\):

| \(n\) | Critical Value |
|-------|----------------|
| 3     | 0.997          |
| 4     | 0.950          |
| 5     | 0.878          |
| 6     | 0.811          |
| 7     | 0.754          |
| 8     | 0.707          |
| 9     | 0.666          |
| 10    | 0.632          |
| 11    | 0.602          |
| 12    | 0.576          |
| 13    | 0.553          |
| 14    | 0.532          |
| 15    | 0.514          |
| 16    | 0.497          |
| 17    | 0.482          |
| 18    | 0.468          |
| 19    | 0.456          |
| 20    | 0.444          |
| 21    | 0.433          |
| 22    | 0.423          |
| 23    | 0.413          |
| 24    | 0.404          |
| 25    | 0.396          |
| 26    | 0.388          |
Transcribed Image Text:**Data on Lyme Disease Cases and Drowning Deaths** The table displays monthly data on the number of Lyme Disease cases and drowning deaths: | Cases of Lyme Disease | Drowning Deaths | Month | |-----------------------|-----------------|-------| | 2 | 0 | J | | 2 | 1 | F | | 3 | 2 | M | | 4 | 1 | A | | 5 | 2 | M | | 15 | 9 | J | | 22 | 17 | J | | 13 | 5 | A | | 6 | 3 | S | | 5 | 3 | O | | 4 | 1 | N | | 1 | 0 | D | **Critical Values for Correlation Coefficient** The table to the right provides the critical values for correlation coefficients based on sample size \(n\): | \(n\) | Critical Value | |-------|----------------| | 3 | 0.997 | | 4 | 0.950 | | 5 | 0.878 | | 6 | 0.811 | | 7 | 0.754 | | 8 | 0.707 | | 9 | 0.666 | | 10 | 0.632 | | 11 | 0.602 | | 12 | 0.576 | | 13 | 0.553 | | 14 | 0.532 | | 15 | 0.514 | | 16 | 0.497 | | 17 | 0.482 | | 18 | 0.468 | | 19 | 0.456 | | 20 | 0.444 | | 21 | 0.433 | | 22 | 0.423 | | 23 | 0.413 | | 24 | 0.404 | | 25 | 0.396 | | 26 | 0.388 |
**Understanding the Correlation Between Lyme Disease and Drowning Deaths**

Lyme disease is an inflammatory disease that leads to symptoms such as skin rash and flu-like conditions. It is transmitted via the bite of an infected deer tick. This exercise presents data reflecting the number of reported Lyme disease cases and drowning deaths in a rural county. You will work through parts (a) through (c) below:

### Tasks:

1. **Draw a Scatter Diagram of the Data**
   - Select the correct graph reflecting the relationship between Lyme disease cases and drowning deaths.

   Options for the scatter diagram:
   - **A:** Lyme Disease on the x-axis, Drownings on the y-axis
   - **B:** Drownings on the x-axis, Lyme Disease on the y-axis
   - **C:** Lyme Disease on the x-axis, Drownings on the y-axis (✓ Correct)
   - **D:** Drownings on the x-axis, Lyme Disease on the y-axis

   The correct scatter plot is option **C**, where Lyme Disease is plotted on the x-axis and Drownings on the y-axis.

2. **Determine the Linear Correlation Coefficient**
   - The linear correlation coefficient (\( r \)) quantifies the strength of the relationship between Lyme disease and drowning deaths.

   Result: \( r = 0.963 \) (Rounded to three decimal places)

3. **Assess the Linear Relationship**
   - Analyze whether there is a significant linear relationship between reported cases of Lyme disease and the number of drowning deaths based on the correlation coefficient.

   **Tasks:**
   - Determine if the variables Lyme disease and drowning deaths are [positively/negatively] associated because \( r \) is [greater/less] than the critical value.

### Analysis:

- The variable coefficients indicate a positive association since the correlation coefficient is high (close to 1), suggesting a strong positive correlation.
- The absolute value of the correlation coefficient \( r \) is likely greater than the critical value, affirming a significant linear relationship.

In summary, this analysis aims to explore the correlation between Lyme disease cases and drowning incidents in a specified county, helping understand potential direct or indirect associations.
Transcribed Image Text:**Understanding the Correlation Between Lyme Disease and Drowning Deaths** Lyme disease is an inflammatory disease that leads to symptoms such as skin rash and flu-like conditions. It is transmitted via the bite of an infected deer tick. This exercise presents data reflecting the number of reported Lyme disease cases and drowning deaths in a rural county. You will work through parts (a) through (c) below: ### Tasks: 1. **Draw a Scatter Diagram of the Data** - Select the correct graph reflecting the relationship between Lyme disease cases and drowning deaths. Options for the scatter diagram: - **A:** Lyme Disease on the x-axis, Drownings on the y-axis - **B:** Drownings on the x-axis, Lyme Disease on the y-axis - **C:** Lyme Disease on the x-axis, Drownings on the y-axis (✓ Correct) - **D:** Drownings on the x-axis, Lyme Disease on the y-axis The correct scatter plot is option **C**, where Lyme Disease is plotted on the x-axis and Drownings on the y-axis. 2. **Determine the Linear Correlation Coefficient** - The linear correlation coefficient (\( r \)) quantifies the strength of the relationship between Lyme disease and drowning deaths. Result: \( r = 0.963 \) (Rounded to three decimal places) 3. **Assess the Linear Relationship** - Analyze whether there is a significant linear relationship between reported cases of Lyme disease and the number of drowning deaths based on the correlation coefficient. **Tasks:** - Determine if the variables Lyme disease and drowning deaths are [positively/negatively] associated because \( r \) is [greater/less] than the critical value. ### Analysis: - The variable coefficients indicate a positive association since the correlation coefficient is high (close to 1), suggesting a strong positive correlation. - The absolute value of the correlation coefficient \( r \) is likely greater than the critical value, affirming a significant linear relationship. In summary, this analysis aims to explore the correlation between Lyme disease cases and drowning incidents in a specified county, helping understand potential direct or indirect associations.
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