You wish to determine if there is a positive linear correlation between the age of a driver and the number of driver deaths. The following table represents the age of a driver and the number of driver deaths per 100,000. Use a significance level of 0.01 and round all values to 4 decimal places. Driver Age Number of Driver Deaths per 100,000 18 35 38 26 18 23 57 36 64 29 80 29 53 36 Ho: p = 0 Ha: p > 0 Find the Linear Correlation Coefficient r Find the p-value A p-value=

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### Exploring Correlation Between Driver Age and Driver Deaths

In this exercise, we aim to determine if there is a positive linear correlation between the age of a driver and the number of driver deaths. The table below presents the relationship between the age of a driver and the number of driver deaths per 100,000 drivers. A significance level of 0.01 will be used for this analysis, and all values will be rounded to four decimal places.

#### Data Table: Driver Age vs. Number of Driver Deaths per 100,000

| **Driver Age** | **Number of Driver Deaths per 100,000** |
|:--------------:|:--------------------------------------:|
| 18             | 35                                     |
| 38             | 26                                     |
| 18             | 23                                     |
| 57             | 36                                     |
| 64             | 29                                     |
| 80             | 29                                     |
| 53             | 36                                     |

#### Hypothesis Testing

- **Null Hypothesis (Ho):** ρ = 0 
- **Alternative Hypothesis (Ha):** ρ > 0

#### Analysis

##### 1. Calculate the Linear Correlation Coefficient
- Denoted as **r**, the linear correlation coefficient will quantify the strength and direction of the linear relationship between driver age and the number of driver deaths.

\[ r = \_ \_ \_ \_ \_ \_ \_ \_ \]

##### 2. Determine the p-value
- The **p-value** will help in testing the null hypothesis. A p-value lower than 0.01 would indicate that we can reject the null hypothesis in favor of the alternative hypothesis, supporting the presence of a positive linear correlation.

\[ p\text{-value} = \_ \_ \_ \_ \_ \_ \_ \_ \]

---

By filling in these values, students will gain insight into statistical methods, specifically linear correlation and hypothesis testing.
Transcribed Image Text:--- ### Exploring Correlation Between Driver Age and Driver Deaths In this exercise, we aim to determine if there is a positive linear correlation between the age of a driver and the number of driver deaths. The table below presents the relationship between the age of a driver and the number of driver deaths per 100,000 drivers. A significance level of 0.01 will be used for this analysis, and all values will be rounded to four decimal places. #### Data Table: Driver Age vs. Number of Driver Deaths per 100,000 | **Driver Age** | **Number of Driver Deaths per 100,000** | |:--------------:|:--------------------------------------:| | 18 | 35 | | 38 | 26 | | 18 | 23 | | 57 | 36 | | 64 | 29 | | 80 | 29 | | 53 | 36 | #### Hypothesis Testing - **Null Hypothesis (Ho):** ρ = 0 - **Alternative Hypothesis (Ha):** ρ > 0 #### Analysis ##### 1. Calculate the Linear Correlation Coefficient - Denoted as **r**, the linear correlation coefficient will quantify the strength and direction of the linear relationship between driver age and the number of driver deaths. \[ r = \_ \_ \_ \_ \_ \_ \_ \_ \] ##### 2. Determine the p-value - The **p-value** will help in testing the null hypothesis. A p-value lower than 0.01 would indicate that we can reject the null hypothesis in favor of the alternative hypothesis, supporting the presence of a positive linear correlation. \[ p\text{-value} = \_ \_ \_ \_ \_ \_ \_ \_ \] --- By filling in these values, students will gain insight into statistical methods, specifically linear correlation and hypothesis testing.
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