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).
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.