A bio-engineering lab measures the concentration of a specific catalyst in batches of synthetic fuel. The concentration levels follow a normal distribution with mean μ\muμ g/L and standard deviation σ\sigmaσ g/L. A random sample of 12 batches is analysed. For this sample, the calculated mean concentration is yˉ=216.5\bar{y} = 216.5yˉ=216.5 and the unbiased estimate of the population variance is s2=58.5s^2 = 58.5s2=58.5.
Test, at the 5% level of significance, whether or not σ\sigmaσ is greater than 5.5. State your hypotheses clearly.
Test, at the 5% level of significance, whether or not μ\muμ is greater than 212.0.
State an assumption about the distribution of catalyst concentrations that is necessary for these tests to be valid.
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.