Question

3b which values could the correlation coefficient take? between -0.2 and 0.2 between 0.8 and 1 between 0.4 and 0.6 between -0.6 and -0.4 between -1 and -0.8

Explanation:

The correlation coefficient (usually denoted as \( r \)) has a range of \(-1 \leq r \leq 1\). All the given intervals (between -0.2 and 0.2, between 0.8 and 1, between 0.4 and 0.6, between -0.6 and -0.4, between -1 and -0.8) lie within the valid range of \([-1, 1]\). So each of these intervals is a possible range for the correlation coefficient. But since the question is asking "which values could the correlation coefficient take" (implying all valid ones among the options), we need to check each:

• Option 1: Between -0.2 and 0.2: Valid, as both endpoints are within \([-1,1]\).
• Option 2: Between 0.8 and 1: Valid, since \( 0.8 \geq -1 \) and \( 1 \leq 1 \).
• Option 3: Between 0.4 and 0.6: Valid, within \([-1,1]\).
• Option 4: Between -0.6 and -0.4: Valid, within \([-1,1]\).
• Option 5: Between -1 and -0.8: Valid, since \(-1 \leq r \leq -0.8\) is within \([-1,1]\).

However, if the question is asking which of these are possible (i.e., all that are within \([-1,1]\)), then all the options (A to E) are correct because their intervals are subsets of \([-1, 1]\). But maybe the question is expecting to recognize that any interval within \([-1,1]\) is possible. So each of the options A, B, C, D, E represents a possible range for \( r \).

Answer:

A. Between \(-0.2\) and \(0.2\), B. Between \(0.8\) and \(1\), C. Between \(0.4\) and \(0.6\), D. Between \(-0.6\) and \(-0.4\), E. Between \(-1\) and \(-0.8\)