The direction and strength of the association between the variables is weak negative. Hence, option D is correct.
Here is the step-by-step calculation of the direction and strength of the association between the variables:
Step 1: Calculate the Spearman correlation coefficient.
The Spearman correlation coefficient is a nonparametric measure of rank correlation that can be used to assess the monotonic relationship between two variables. It is calculated as follows:
rho = 1 - (6 * Σd^2) / (n^3 - n)
where:
* rho is the Spearman correlation coefficient
* d is the difference in ranks between the two variables for each observation
* n is the number of observations
In this case, we have n = 8 observations. We can calculate the difference in ranks and the squared differences as follows:
| Training Hours | Accidents | Rank (Training Hours) | Rank (Accidents) | d | d^2 |
| --- | --- | --- | --- | --- | --- |
| 0 | 6 | 1 | 8 | 7 | 49 |
| 12 | 0 | 8 | 1 | 7 | 49 |
| 2 | 5 | 2 | 5 | -3 | 9 |
| 10 | 1 | 7 | 2 | 5 | 25 |
| 9 | 2 | 6 | 3 | 3 | 9 |
| 5 | 2 | 4 | 3 | 1 | 1 |
| 6 | 2 | 5 | 3 | 2 | 4 |
| 4 | 3 | 3 | 4 | -1 | 1 |
Next, we can plug these values into the formula for the Spearman correlation coefficient:
rho = 1 - (6 * 141) / (8^3 - 8)
rho = -0.54
Step 2: Interpret the correlation coefficient.
The Spearman correlation coefficient ranges from -1 to 1. A value of -1 indicates a perfect negative monotonic relationship, meaning that as one variable increases, the other variable decreases. A value of 1 indicates a perfect positive monotonic relationship, meaning that as one variable increases, the other variable also increases. A value of 0 indicates no monotonic relationship between the two variables.
In this case, the Spearman correlation coefficient is -0.54, which indicates a moderate negative monotonic relationship between training hours and accidents. This means that as training hours increase, accidents tend to decrease.
Step 3: Determine the direction and strength of the association.
Based on the interpretation of the correlation coefficient, we can determine that the direction of the association is negative and the strength of the association is moderate.
Therefore, the answer is D) weak negative.