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.
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.