In the past, the annual amount of wheat produced per farm by a large number of similar sized farms in a certain region had mean 24.0 tonnes and standard deviation 5.2 tonnes. Last summer a new fertiliser was used by all the farms, and it was expected that the mean amount of wheat produced per farm would be greater than 24.0 tonnes. In order to test whether this was true, a scientist recorded the amounts of wheat produced by a random sample of 50 farms last summer. He found that the value of the sample mean was 25.8 tonnes. Stating a necessary assumption, carry out the test at the 1% significance level.

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

1. [B1] Assume SD still = 5.2 (OE i.e. 'Assume the SD remains unchanged'.)
2. [B1] H₀: μ = 24.0 H₁: μ > 24.0 (Or population mean; not just mean.)
3. [M1] (25.8-24.0) / (5.2/√50) (For standardising (could be implied). Must have √50.)
4. [A1] = 2.448 (Or P(X̄ > 25.8) = 0.0071 .)
5. [M1] '2.448' > 2.326 (Or 0.0071 < 0.01. For valid comparison.)
6. [A1FT] [Reject H₀] There is evidence that (mean) amount of wheat is greater. (OE. FT their Zcalc. In context, not definite, eg not ‘Mean amount of wheat is greater’ No contradictions. CV method: CV= 25.71 M1A1 25.71<25.8 M1 A1FT or CV=24.09 M1 A1 24.09>24 M1 A1FT.)