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.
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.