What can you conclude if the true correlation coefficient is between -0.9095 and -0.8019?

When evaluating the correlation coefficient, it's important to understand what the values signify in terms of the strength and direction of the relationship between two variables. The correlation coefficient ranges from -1 to +1, where a value of -1 indicates a perfect negative correlation, 0 indicates no correlation, and +1 indicates a perfect positive correlation.

A correlation coefficient that falls between -0.9095 and -0.8019 indicates a strong negative correlation. This range suggests that as one variable increases, the other variable tends to decrease significantly, and vice versa. The closer the coefficient is to -1, the stronger the negative relationship between the two variables. Therefore, when you see a value in this range, it indicates a robust inverse relationship, which is why the conclusion is that there is a strong negative correlation present.

By contrast, a strong positive correlation would have values between 0.8019 and 0.9095, while a weak negative correlation would range closer to 0 (but still negative), indicating a much weaker relationship. Similarly, no correlation would mean the coefficient is around 0, indicating no relationship at all. Thus, the conclusion regarding the correlation coefficient in question directly matches the definition of a strong negative correlation.