In the past, the mean height of plants of a particular species has been 2.3m. A random sample of 60 plants of this species was treated with fertiliser and the mean height of these 60 plants was found to be 2.4 m. Assume that the standard deviation of the heights of plants treated with fertiliser is 0.4 m.

Mark scheme

Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.

1. [B1] H0: Pop mean height = 2.3 H1: Pop mean height > 2.3 Not just 'mean' Allow μ
2. [M1] For standardising, must have √60
3. [A1] 1.936 or 1.937 or 1.94
4. [M1] Valid comparison with 1.96 Or 2.64% > 2.5% OE Accept 1.936 < 2.24 or 2.64% > 1.25% OE if H₁μ ≠ 2.3
5. [A1 FT] [Do not reject Ho] No evidence that (mean) height (with fertiliser) is more than without In context, not definite. E.g. not 'Mean height is not greater' with no contradictions No FT for 2 tail test (max B0 M1 A1 M1 A0 3/5) Accept critical values method 2.401 (M1 A1) 2.4 < 2.401 (M1) Condone 2.299 (M1 A1) < 2.3 (M1) Al conclusion