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.
Practise Edexcel A Level Maths Hypothesis Testing with the Normal Distribution with exam-style questions for A Level Maths. 132 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
