2025 CJC P2 Q9
2025 CJC P2 Q9
9 marks
A teacher conducts a survey on \(7\) students to investigate the relationship between the number of hours \((h)\) of “screen-time” per week and the average scores \((s)\) they obtained in a recently concluded examination She records her findings as shown in the following table.
| \(h\) | \(8.5\) | \(14\) | \(20\) | \(27\) | \(10.5\) | \(17\) | \(23\) |
|---|---|---|---|---|---|---|---|
| \(s\) | \(68\) | \(61\) | \(44\) | \(12\) | \(\alpha\) | \(58\) | \(31\) |
- Given that the regression line of \(s\) on \(h\) is \(s=-3.00799h+100.27974\), show that \(\alpha=67.0\).[2]
- Draw a scatter diagram for the data.[1]
- Explain why \(s=kh^2+c\) is the better model compared to the one in part (a), by giving appropriate reasons. State the values of \(k\) and \(c\).[3]
- Using the better model, estimate the score a student can expect to obtain if he spends \(7\) hours of screen-time a week. Comment on the reliability of the estimate obtained.[2]
- The teacher observes a trend from her findings and concludes with a statement: Increased screen-time will cause the exam scores to decrease. Comment on the validity of the statement.[1]
Solution:
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Answer:(a) \(\alpha\approx67.0\) (shown). (b) Scatter shown. (c) \(k\approx-0.0873\), \(c\approx77.7\); curved scatter and \(r_{h^2,s}\approx-0.991\) support the model. (d) \(73.4\); extrapolation below the data range. (e) Correlation does not establish causation.
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