A specialized polymer resin is engineered to have a mean curing time of 142.5 minutes. A chemical engineer suspects that a recent change in the catalyst's purity has led to an increase in the mean curing time. To investigate this, a random sample of 12 batches is selected, and the curing times, t t\,t minutes, are recorded. The following summary statistics were obtained:
∑t=1758.0,∑t2=257767.0 \sum t = 1758.0, \quad \sum t^2 = 257767.0 ∑t=1758.0,∑t2=257767.0Stating your hypotheses clearly, test at the 1% level of significance whether there is evidence that the mean curing time has increased. You should assume that the curing times follow a normal distribution and that the sample variance is a valid estimate of the population variance.
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.