To determine the correlation coefficient for the given data, first we need to understand the data itself:
| Year | Time (seconds) |
|------|-----------------|
| 1 | 98 |
| 2 | 101 |
| 3 | 109 |
| 4 | 117 |
| 5 | 119 |
| 6 | 127 |
### Step-by-Step Process:
1. Sketch the Scatter Plot:
- Plot the Year on the x-axis and the Time on the y-axis.
- Each year corresponds to a specific time.
2. Interpreting the Data:
- As the years increase, the times also appear to increase.
- This suggests a positive correlation between year and time.
3. Calculating the Correlation Coefficient:
- The calculation of the correlation coefficient measures the strength and direction of the linear relationship between two variables.
- Without going into the detailed computations, notice the scatter plot's pattern: a strong, positive linear trend.
4. Choosing the Correct Answer:
- Option A: 0.20 (This suggests a weak positive correlation)
- Option B: 0.99 (This indicates a very strong positive correlation)
- Option C: 0.20 (same as Option A, likely an error)
- Option D: -0.83 (This indicates a strong negative correlation)
- Option E: -1.01 (This is outside the valid range for correlation coefficients, which is from -1 to 1)
### Conclusion:
Since our data shows a strong positive correlation (as times increase almost linearly with years), the correlation coefficient closest to this description is [tex]\( B. 0.99 \)[/tex].
Thus, the correct answer is: B. 0.99.
