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.
162 exam-style questions on AQA A Level Maths 2.5 O: Statistical hypothesis testing, covering 2.5.1 Language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, and 2.5.3 Hypothesis test for a Normal mean (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.