Final answer:
The correlation coefficient must be between -1 and 1 to be valid. A value of -8.16 indicates an error, and if the correct value is within the possible range and significantly different from zero, the linear relationship is significant.
Step-by-step explanation:
You asked whether a sample of 36 patients yielding a correlation coefficient of -8.16 is sufficiently large to conclude that a linear relationship exists. The correlation coefficient (r) should be between -1 and 1. A value like -8.16 is not possible, indicating there may have been an error either in the computation or transcription of the coefficient. For a coefficient to be significant, it needs to be significantly different from zero, and within the correct range. For example, if a computed correlation coefficient was -0.816 instead of -8.16, and depending on the degrees of freedom (which would be n - 2 for a correlation test), you could conclude it is significant if it is outside the range provided in critical value tables at a certain confidence level (like 95%). If r is outside the critical values at the chosen alpha level, typically 0.05, we reject the null hypothesis H0 and conclude there is a significant linear relationship.