A specialty coffee roaster claims that their 'Dark Peak' espresso beans contain an average of 14.5 mg of caffeine per gram. A food scientist suspects that recent inconsistencies in roasting temperatures have altered this mean caffeine content. A random sample of 8 grams of beans is analyzed, and the caffeine concentration ccc (in mg/g) for each is recorded below:
14.6,14.9,15.1,14.7,14.5,15.0,14.8,14.8 14.6, \quad 14.9, \quad 15.1, \quad 14.7, \quad 14.5, \quad 15.0, \quad 14.8, \quad 14.8 14.6,14.9,15.1,14.7,14.5,15.0,14.8,14.8Conduct a hypothesis test at the 10% significance level to investigate the scientist's suspicion. You may assume that caffeine concentrations are normally distributed with a standard deviation of 0.4 mg/g.
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.