An agricultural scientist monitors the yield of a variety of wheat. Past records show that the yield per plot is normally distributed with mean 42.0 kg and standard deviation 4.5 kg.
A new fertiliser is introduced, and it is claimed that the mean yield per plot has changed. A random sample of 64 plots is treated with the new fertiliser, and the total yield for these 64 plots is 2760 kg.
In this question you must show detailed reasoning.
Stating your hypotheses clearly, test this claim at the 5% significance level. You may assume that the yields are still normally distributed with standard deviation 4.5 kg.
390 exam-style questions on OCR A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.