3 In the past, the mean time taken by Freda for a particular daily journey was 39.2 minutes. Following the introduction of a one-way system, Freda wishes to test whether the mean time for the journey has decreased. She notes the times, \(t\) minutes, for 40 randomly chosen journeys and summarises the results as follows.
$$n = 40 \quad \Sigma t = 1504 \quad \Sigma t ^ { 2 } = 57760$$
- Calculate unbiased estimates of the population mean and variance of the new journey time.
- Test, at the \(5 \%\) significance level, whether the population mean time has decreased.