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.
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.