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.
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.