Final Answer:
The best prediction for the value of ( r ) for the data with the added outlier is A) -0.59.
Step-by-step explanation
When determining the effect of an outlier on the correlation coefficient (( r )), it is essential to consider the impact of the outlier on the overall pattern of the data. In this case, since the original data set without the outlier has ( r = -0.92 ), a negative value, the outlier is likely to decrease the correlation. Among the given options, -0.59 is the closest negative value to the original ( r ) and is the best prediction for the correlation coefficient with the added outlier.
To understand this, one can visualize how an outlier, especially one with a different trend or direction, can influence the correlation. If the outlier introduces a positive correlation, ( r ) would move closer to 0, while a negative correlation would bring ( r ) closer to -1. Therefore, the best prediction is a negative value, and -0.59 aligns with this expectation, being the closest to the original ( r = -0.92 ).
In conclusion, selecting -0.59 as the best prediction accounts for the tendency of an outlier to diminish the strength of correlation in a negative direction. This choice is a reasonable estimate based on the given original ( r ) value and the impact of the outlier on the correlation coefficient.