The mass of a high-precision turbine blade is modelled by a normal distribution with a mean of 450.0450.0450.0 g and a standard deviation of 12.412.412.4 g. After a change in the manufacturing process, a quality control engineer suspects that the mean mass of the blades has decreased. A random sample of 505050 blades is measured, and the sample mean mass is found to be 446.2446.2446.2 g. Carry out a hypothesis test at the 2%2\%2% significance level to investigate the engineer's suspicion.
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.