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.
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.