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.
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.