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.