2024 ACJC H1 Q10
2024 ACJC H1 Q10
8 marks
A horticulturist carries out research on the effects of varying amounts of fertilizer on the average crop yield of potatoes. Eight potato plants of the same variety were selected at random. The results are shown in the table below.
| Plant | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) |
|---|---|---|---|---|---|---|---|---|
| Amount of fertiliser (\(x\) grams per square metre) | \(3.2\) | \(1.5\) | \(0.8\) | \(0\) | \(2.5\) | \(8.0\) | \(4.0\) | \(4.1\) |
| Average crop yield (\(y\) kilograms) | \(2.6\) | \(2.2\) | \(2.3\) | \(2.0\) | \(2.3\) | \(3.6\) | \(2.7\) | \(2.8\) |
- Give a sketch of the scatter diagram of the data.[2]
- Find the product moment correlation coefficient, \(r\), and comment on its value in the context of the data.[2]
- Find the equation of the regression line of \(y\) on \(x\) in the form \(y = a + bx\), giving the values of \(a\) and \(b\) correct to \(3\) significant figures.[1]
- Use the equation of your regression line to estimate the amount of fertiliser used on a potato plant of the same variety when the average crop yield of potatoes is \(2.5\) kilograms. Comment on the reliability of the estimate.[2]
- Without any further calculations, explain briefly what will happen to the value of \(r\) found in (ii) if \(y\) was recorded in grams instead.[1]
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Answer:(ii)r=0.980
(iii)\(y=1.97+0.196x\)
(iv)x=2.7g/m\(^2\)
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