Healthy-Greens Farm grows organic cucumbers. They are considering a new irrigation system and hope it will increase the average yield per plant by at least 1.5 kg. The variance of the yield using the existing system is 0.6 kg2, and the variance of the yield using the new system is 0.8 kg2. A random sample of 50 plants using the existing system has a mean yield of 6.2 kg. A random sample of 80 plants using the new system has a mean yield of 8.1 kg.
Stating your hypotheses clearly, test at the 5% level of significance whether or not there is evidence that the mean yield with the new system is more than 1.5 kg greater than the mean yield with the existing system.
Explain the relevance of the Central Limit Theorem to the test conducted in part (a).
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.