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.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.