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.
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.