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.