A materials scientist is evaluating the tensile strength of two newly developed carbon-fiber composites: 'Aeroflex' and 'Durawave'. The scientist believes that Aeroflex has a mean tensile strength that is more than 50 MPa greater than that of Durawave.
A random sample of 200 specimens of Aeroflex found a mean tensile strength of 3452 MPa with a standard deviation of 78 MPa.
A random sample of 250 specimens of Durawave found a mean tensile strength of 3384 MPa with a standard deviation of 72 MPa.
Stating your hypotheses clearly, test the scientist's claim at the 5% level of significance.
State whether it was necessary to assume that the tensile strengths of the specimens are normally distributed. Give a reason for your answer.
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.