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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.