2024 SAJC H1 Q10
2024 SAJC H1 Q10
10 marks
The table below gives the age and weight for \(10\) broiler chicks.
| Age (days), \(x\) | 18 | 1 | 10 | 14 | 13 | 15 | 17 | 12 | 16 | 20 |
|---|---|---|---|---|---|---|---|---|---|---|
| Weight (grams), \(y\) | 108 | 44 | 66 | 84 | 80 | 92 | 100 | 76 | 104 | 118 |
- Give a sketch of the scatter diagram for the data, as shown on your calculator.[2]
- Find the product moment correlation coefficient.[1]
- State whether we should use the \(x\) on \(y\) line or the \(y\) on \(x\) line to calculate an estimate for the age of a broiler chick which weighs \(55\) grams. Justify your choice of line.[2]
- Using the regression line you have chosen in part (iii), calculate an estimate for the age of a broiler chick which weighs \(55\) grams. Sketch this line on your scatter diagram in part (i).[3]
- Explain why you would expect this estimate in part (iv) to be reliable.[2]
Solution:
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Answer:(i) Scatter diagram shown. (ii) \(r\approx0.970\). (iii) Growth-model assumption: \(y\) on \(x\); direct prediction of age: \(x\) on \(y\). (iv) Growth-model calibration: \(5.58\) days; direct age-on-weight prediction: \(6.05\) days. (v) Within the observed weight range, with strong linear association.
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