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.
209 exam-style questions on CCEA A Level Maths 4.6 Statistical hypothesis testing (A-level only), covering 4.6.1 Statistical hypothesis testing (A-level only), 4.6.2 Statistical hypothesis testing (A-level only), 4.6.3 Statistical hypothesis testing (A-level only), 4.6.4 Statistical hypothesis testing (A-level only), and 4.6.5 Statistical hypothesis testing (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.