A study was conducted on a group of pre-diabetic seniors to examine whether the number of hours of e

Question

A study was conducted on a group of pre-diabetic seniors to examine whether the number of hours of exercise per week ($t$) has any effect on their fasting blood sugar levels ($S$, measured in mg/dL). The results were as follows.

$t$	$1.5$	$1.8$	$2.1$	$2.4$	$2.5$	$3.1$	$3.5$	$4.2$
$S$	$119$	$108$	$100$	$95$	$93$	$88$	$86$	$85$

Draw the scatter diagram for these values, labelling the axes.[1]
Comment on whether a linear model would be appropriate, referring both to the scatter diagram and the context of the question.[2]
By considering the shape of the following graphs, explain which model is the most appropriate for the data collected, where $a$ and $b$ are positive constants.[1]

$\mathbf{A}: S=a+bt^2, \quad \mathbf{B}: S=a+\frac{b}{t}, \quad \mathbf{C}: S=a+b \ln t$

Using the appropriate model selected above, find

the value of the product moment correlation coefficient,[1]
the equation of the regression line of $S$ on $t$, and hence find an estimate of the exercise time required for the fasting blood sugar to be $99$ mg/dL. Comment on the reliability of your answer.[3]

Accepted Answer

(c) Model B (d) $r=0.988$ (e) $S=62.4+\dfrac{81.7}{t}$, $t=2.23$ hours

2025 ASRJC P2 Q8

2025 ASRJC P2 Q8

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