To determine which correlation coefficient indicates a weak negative correlation, let's review each of the provided options:
1. Option A: [tex]\( r = 0.5 \)[/tex]
- This value represents a positive correlation, not a negative one.
2. Option B: [tex]\( r = -2.0 \)[/tex]
- A correlation coefficient, [tex]\( r \)[/tex], must lie between -1 and 1. Therefore, [tex]\( r = -2.0 \)[/tex] is not a valid correlation coefficient.
3. Option C: [tex]\( r = -0.8 \)[/tex]
- This value represents a strong negative correlation, as it is close to -1 and indicates that the relationship between the variables is strongly negative.
4. Option D: [tex]\( r = -0.2 \)[/tex]
- This value represents a weak negative correlation. It is close to 0, showing that the relationship between the variables is negative but not strong.
Given these explanations, the correlation coefficient that indicates a weak negative correlation is:
[tex]\[ \boxed{r = -0.2} \][/tex]
Thus, the correct choice is D. [tex]\( r = -0.2 \)[/tex].
