A civil engineer is testing the load-bearing capacity of a new alloy beam. The design specification requires a mean breaking load of 80.0 kN. The engineer suspects the mean breaking load has decreased and selects a random sample of 50 beams to test this claim. The breaking loads, in kN, are denoted by xxx and the following summary statistics were obtained:
∑x=3992.5,∑x2=318810.5 \sum x = 3992.5, \quad \sum x^2 = 318810.5 ∑x=3992.5,∑x2=318810.5Stating your hypotheses clearly, test at the 1% level of significance whether there is evidence that the mean breaking load of the beams is less than 80.0 kN. You may assume that the breaking loads follow a normal distribution.
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.