An agricultural scientist monitors the growth of a specific variety of wheat. Past data shows that the mean yield per plot is 42.0 kg with a standard deviation of 4.5 kg.
Following the introduction of a new fertilizer, it is claimed that the mean yield of this wheat variety has changed. To test this claim, a random sample of 64 plots is treated with the new fertilizer.
The total yield for these 64 plots is 2758.4 kg.
Assuming that the yields are normally distributed, test at the 5% significance level the claim that the mean yield has changed.
162 exam-style questions on AQA A Level Maths 2.5 O: Statistical hypothesis testing, covering 2.5.1 Language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, and 2.5.3 Hypothesis test for a Normal mean (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.