An agricultural scientist claims that the mean yield of a new variety of wheat, the 'Aureum', is more than 6.5 tonnes per hectare. To test this claim, the scientist measures the yield, xxx, of a random sample of 25 plots and obtains the following statistics:
xˉ=6.81,s=0.75 \bar{x} = 6.81, \quad s = 0.75 xˉ=6.81,s=0.75The yield may be assumed to be normally distributed.
Stating your hypotheses clearly and using a 5% level of significance, test the scientist's claim.
The standard deviation of the yield for a standard wheat variety is 0.6.
Stating your hypotheses clearly, test at the 5% level of significance whether or not there is evidence that the variance of the yield for the Aureum variety is different from that of the standard variety.
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.