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.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.