1 The time taken for Samuel to drive home from work is distributed with mean 46 minutes. Samuel discovers a different route and decides to test at the \(5 \%\) level whether the mean time has changed. He tries this route on a large number of different days chosen randomly and calculates the mean time.

1. State the null and alternative hypotheses for this test.
2. Samuel calculates the value of his test statistic \(z\) to be - 1.729 . What conclusion can he draw?