Final answer:
The sample correlation coefficient r measures the strength and direction of a linear relationship between two variables. It ranges from -1 to +1, where values close to -1 or +1 indicate a strong relationship, and a value close to 0 indicates a weak or no relationship. Without specific data, we cannot determine the exact value of r, but we can say that -14 is incorrect since it's outside the valid range.
The correct answer is A.
Step-by-step explanation:
The sample correlation coefficient, represented as r, is a statistical measure that evaluates the strength and direction of the linear relationship between two quantitative variables. The value of r always lies between -1 and +1. When assessing the strength of the correlation, values close to -1 or +1 indicate a stronger linear relationship, whereas a value close to 0 indicates a weak or no linear relationship.
Given the options in the provided context, r cannot be determined without specific sample data. However, based on general properties of the correlation coefficient, choice (c) -14 cannot be correct since it falls outside the range of possible values for r. If we had the actual data, we could compute r using the appropriate statistical formulas.
To determine which correlation coefficient indicates the strongest relationship between two variables, we look for the value that is closest to -1 or 1. In the given options, -.90 shows a stronger negative relationship compared to -.50. Therefore, answer (a) -.90 would indicate the strongest relationship.
If we are to determine significance and predictive power of the correlation coefficient, we often refer to critical value tables and look for a significant level (p-value) based on the sample size. A significant r value suggests that the line of best fit can be used to predict future outcomes. For example, if we have r = -0.567 for a sample size of 19, we'd consult a table or use statistical software to determine if this r value is significant.