To determine which correlation coefficient indicates a strong positive correlation, let's review the concept of correlation coefficients.
A correlation coefficient (denoted as [tex]\( r \)[/tex]) measures the strength and direction of a linear relationship between two variables. The value of [tex]\( r \)[/tex] ranges from -1 to +1:
- [tex]\( r = +1 \)[/tex] indicates a perfect positive linear relationship.
- [tex]\( r = -1 \)[/tex] indicates a perfect negative linear relationship.
- [tex]\( r = 0 \)[/tex] indicates no linear relationship.
- Values of [tex]\( r \)[/tex] closer to +1 indicate a stronger positive correlation.
- Values of [tex]\( r \)[/tex] closer to -1 indicate a stronger negative correlation.
Now let's evaluate each option given:
A. [tex]\( r = -0.09 \)[/tex]
- This value is slightly negative, indicating a very weak negative correlation. It is not a strong positive correlation.
B. [tex]\( r = +0.5 \)[/tex]
- This value is moderately positive, indicating a moderate positive correlation. While it shows some positive correlation, it is not strong.
C. [tex]\( r = +0.9 \)[/tex]
- This value is very close to +1, indicating a very strong positive correlation.
D. [tex]\( r = -0.1 \)[/tex]
- This value is slightly negative, indicating a very weak negative correlation. It is not a strong positive correlation.
Among the given options, [tex]\( r = +0.9 \)[/tex] is the closest to +1, indicating the strongest positive correlation.
Hence, the correlation coefficient that indicates a strong positive correlation is:
[tex]\[ \boxed{r = +0.9} \][/tex]
