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.
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.