The weights of a random sample of 100 organic apples from an orchard had a mean of 185 g and a standard deviation of 12 g. The weights of a second random sample of 150 non-organic apples from the same orchard had a mean of 188 g and a standard deviation of 15 g.
Test, using a 5% level of significance, whether or not the mean weight of organic apples is less than the mean weight of non-organic apples. State your hypotheses clearly.
State two assumptions you made in carrying out the test in part (a).
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.