Question 1
The correlation coefficient for the association between a car’s age and its fuel efficiency is $r=-0.93$.
The association is best described as
That is it. Step through the hints below to see why.
Not quite. You dropped the negative sign: $r=-0.93$ is below 0, so the association is negative.
Not quite. You read the negative sign as weakness. Strength comes from $|r|=0.93$, which is strong.
Not quite. You made both errors: you called the association weak and dropped the negative sign.
Band words follow a teaching convention, not the syllabus: $|r|\geq0.75$ strong, 0.5 to 0.75 moderate, 0.25 to 0.5 weak, below 0.25 no association.
Choose an option to test its two words against $r=-0.93$.
Direction: $r=-0.93$ is below 0, so the association is negative. Option () says : .
Strength: $|r|=0.93\geq0.75$, so the association is strong. Option () says : .
Both words match, so (A) describes the association.
(B) gets the strength right but the direction wrong: the sign of $r$ is negative.
(C) gets the direction right but the strength wrong: $|r|=0.93$ is strong.
(D) gets both words wrong: the association is negative and strong.
Try the question first. Choose a hint above when you want one.
$r=-0.93$ is negative, so fuel efficiency decreases as the car’s age increases.
$|r|=0.93\geq0.75$, so the association is strong. (Strength words here follow a teaching convention, not the syllabus: $|r|\geq0.75$ strong, 0.5 to 0.75 moderate, 0.25 to 0.5 weak, below 0.25 no association.)
The sign of $r$ gives the direction and the size of $|r|$ gives the strength.
$r=-0.93$ is negative and $|r|=0.93\geq0.75$, so the association is strong and negative.
Only mark this done when you could do it without help. Reading the solution does not count.
A Tangent Tuition mock exam question. It is not a past QCAA question, and Tangent Tuition is not affiliated with the QCAA.
Spot a mistake on this page? Report it