The areas, X cm², of petals of a certain kind of flower have mean µ cm². In the past it has been found that μ = 8.9. Following a change in the climate, a botanist claims that the mean is no longer 8.9. The areas of a random sample of 200 petals from this kind of flower are measured, and the results are summarized by Σx = 1850, Σx² = 17 850.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

1. [B1] est(µ) = 1850/200 or 9.25
2. [M1] Correct formula for unbiased variance estimation and calculation for est(σ²)
3. [A1] est(σ²) = 3.71 (3sf) or 3.7060 or 1475/398
4. [B1] H₀: µ = 8.9 and H₁: µ ≠ 8.9
5. [M1] Calculate test statistic using correct formula (x_bar - mu_0) / (s/sqrt(n))
6. [A1] Test statistic = 2.57 (3sf) or equivalent p-value from 0.00507 – 0.0051
7. [M1] Compare test statistic with critical value (2.240/2.241) or p-value (0.00507-0.0051) with significance level (0.0125)
8. [A1 FT] Reject H₀. There is evidence that µ is not 8.9 (in context, not definite, no contradictions).