A manufacturing process for high-precision optical lenses is designed to produce lenses with a mean thickness of 2.450 mm. The thickness of a lens is known to follow a normal distribution with a standard deviation of 0.012 mm. A quality inspector suspects that the process is malfunctioning and producing lenses that are on average too thin. A random sample of 16 lenses is taken, and the sum of their thicknesses is calculated as ∑x=39.088\sum x = 39.088∑x=39.088 mm.
Stating your hypotheses clearly, test at the 1% significance level whether or not the inspector's suspicion is supported.
162 exam-style questions on AQA A Level Maths 2.5 O: Statistical hypothesis testing, covering 2.5.1 Language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, and 2.5.3 Hypothesis test for a Normal mean (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.