A manufacturer of high-pressure gas cylinders specifies that the internal pressure of a standard unit is normally distributed with a mean of 150.0 kPa and a standard deviation of 4.0 kPa. Following a system maintenance overhaul, a random sample of 16 cylinders is inspected. The internal pressures, p p\,p kPa, for this sample are summarized by the following statistics:
∑p=2419.2∑p2=366050 \sum p = 2419.2 \quad \sum p^2 = 366050 ∑p=2419.2∑p2=366050By stating your hypotheses clearly, test at the 5% significance level whether there is evidence to suggest that the standard deviation of the cylinder pressures has changed.
Stating your hypotheses clearly, test at the 5% significance level whether the mean internal pressure has changed from its original value of 150.0 kPa, using: (i) a normal distribution, (ii) a ttt-distribution.
Using your findings from parts (a) and (b), comment on the mean pressure of the cylinders following the maintenance overhaul, providing a reason for your choice of test.
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.