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.
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.