In the past, Freda’s mean time for a particular daily journey was 39.2 minutes. Following the introduction of a one-way system, she wishes to test whether the mean journey time has decreased. For 40 randomly chosen journeys, with times \(t\) minutes, \[n=40,\qquad\sum t=1504,\qquad\sum t^2=57760.\]

(a) Calculate unbiased estimates of the population mean and variance of the new journey time. [3]

(b) Test, at the 5% significance level, whether the population mean time has decreased. [5]