Question

Which of the following statements is false when comparing two sets of data when the correlation coefficient is —0. 8?

A. The lines for each set of data slope from top left to bottom right.
B. For both sets of data, there is a negative relationship, but no cause and effect indicated.
C. The two datasets must be identical.
D. The plots of each set of datapoints may not be identical.

Answer 1

The false statement when comparing two sets of data with a correlation coefficient of -0.8 is that the two datasets must be identical. In reality, datasets can have the same correlation coefficient but differ in their specific data points and distributions.

Step-by-step explanation:

When comparing two sets of data with a correlation coefficient of —-0.8, it is important to identify the false statement among the provided options. A correlation coefficient value in this range suggests a strong negative relationship between the two variables. This means that as one variable increases, the other tends to decrease, and vice versa.

A. The statement is true; since the correlation is negative, the lines would slope from the top left to the bottom right on a scatter plot.

B. This statement is also true; a correlation coefficient by itself does not imply causation but rather indicates the strength and direction of a linear relationship between two variables.

C. The statement that the two datasets must be identical is false. Two sets of data can have the same correlation coefficient but can be different in terms of the actual data points and their spread.

D. This statement is true as well; the plots of each set of data points may not be identical since different datasets can have the same correlation coefficient but differ in their distributions.