In the past, the time, in hours, for a particular train journey has had mean 1.40 and standard deviation 0.12. Following the introduction of some new signals, it is required to test whether the mean journey time has decreased.

(a) State what is meant by a Type II error in this context. [1]

(b) The mean time for a random sample of 50 journeys is found to be 1.36 hours.

(b) Assuming that the standard deviation of journey times is still 0.12 hours, test at the 2.5% significance level whether the population mean journey time has decreased. [5]

(c) State, with a reason, which of the errors, Type I or Type II, might have been made in the test in part (b). [2]