A factory produces metal rods with a target mean length of 12 cm. A quality control manager suspects the mean length has decreased and selects a random sample of 8 rods to test this claim. The lengths, in cm, are denoted by xxx and the following summary statistics were obtained:
∑x=94.4,∑x2=1114.2 \sum x = 94.4, \quad \sum x^2 = 1114.2 ∑x=94.4,∑x2=1114.2Stating your hypotheses clearly, test at the 5% level of significance whether there is evidence that the mean length of the rods is less than 12 cm. You may assume that the lengths of the rods 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.