In the past, the mean length of a particular variety of worm has been 10.3 cm, with standard deviation 2.6cm. Following a change in the climate, it is thought that the mean length of this variety of worm has decreased. The lengths of a random sample of 100 worms of this variety are found and the mean of this sample is found to be 9.8 cm. Assuming that the standard deviation remains at 2.6cm, carry out a test at the 2% significance level of whether the mean length has decreased.

Mark scheme

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

1. [B1] Ho: Population mean length = 10.3 cm H1: Population mean length < 10.3 cm or μ = 10.3 (not just 'mean'). μ < 10.3
2. [M1] If ± 1.923 (or 0.0272) seen allow M1 implied.
3. [A1] z = -1.923 Accept ± . Accept 3sf.
4. [M1] -1.923 > -2.054 or -2.055 OE For a valid comparison. Or compare 1 – Φ('1.923') with 0.02 e.g. 0.0272 > 0.02 Use of CV 9.8 > 9.766 scores M1 A1 for 9.766 and M1 for comparison.
5. [A1 FT] [Not reject Ho] No evidence that [mean] length has decreased FT their z. No contradictions, not definite, in context.