A company produces steel rods whose lengths follow a normal distribution with mean μ\muμ cm and standard deviation σ\sigmaσ cm. A random sample of 16 rods is measured. From this sample, the unbiased estimate of the mean is xˉ=122.4\bar{x} = 122.4xˉ=122.4 and the unbiased estimate of the variance is s2=3.84s^2 = 3.84s2=3.84.
Test, at the 5% level of significance, whether or not σ\sigmaσ is greater than 1.5. State your hypotheses clearly.
Test, at the 5% level of significance, whether or not μ\muμ is greater than 121.5.
State an assumption about the distribution of rod lengths 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.