The heights of one-year-old trees of a certain variety are known to have mean 2.3 m. A scientist believes that, on average, trees of this age and variety in her region are slightly taller than in other places. She plans to carry out a hypothesis test, at the 2% significance level, in order to test her belief.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

1. 0.02 or 2%
2. H₀: μ = 2.3 H₁: μ > 2.3
3. s² = 1/99 (580 - 238²/100) or 1/99 (580 - (238/100)²)
4. = 0.137 = 113/825 or s = 0.370 (3 sf) and x̅ = 238/100 [= 2.38]
5. z = (2.38-2.3) / √('0.137'/100) [=2.161 or 2.162]
6. = 2.16 (3 sf) OR 0.0153/0.0154 if area comparison used
7. '2.16' > 2.054 (or 2.055) OR ‘0.0153 or 0.0154'<0.02
8. [There is evidence to reject H₀.] / There is sufficient evidence to suggest that the [mean] height [in scientist's region] is greater than 2.3 [m] OR there is sufficient evidence to suggest that the scientist's claim is justified.
9. Not possible since H₀ was rejected. / Follow through their conclusion in (b) . / Condone a definite statement.