The concentration of a catalytic agent used in a batch manufacturing process is modeled by a normal distribution with a mean of 145.0145.0145.0 ppm and a standard deviation of 12.412.412.4 ppm. A quality control technician suspects that a change in raw material sourcing has led to a reduction in the mean concentration. A random sample of 505050 batches is analyzed, and the sample mean concentration is found to be 141.2141.2141.2 ppm.
Carry out a hypothesis test at the 2%2\%2% significance level to investigate the technician'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.