A researcher investigates the yield of two varieties of wheat, Variety X and Variety Y. They believe that Variety X has a higher mean yield than Variety Y. A random sample of 60 plots of Variety X produced a mean yield of 445 kg with a standard deviation, sXs_XsX, of 32 kg. Another random sample of 75 plots of Variety Y produced a mean yield of 432 kg with a standard deviation, sYs_YsY, of 24 kg.
Stating your hypotheses clearly and using a 5% level of significance, test whether or not the researcher's belief is supported by the data.
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.