7 In the past Laxmi's time, in minutes, for her journey to college had mean 32.5 and standard deviation 3.1. After a change in her route, Laxmi wishes to test whether the mean time has decreased. She notes her journey times for a random sample of 50 journeys and she finds that the sample mean is 31.8 minutes. You should assume that the standard deviation is unchanged.

1. Carry out a hypothesis test, at the \(8 \%\) significance level, of whether Laxmi's mean journey time has decreased.
   Later Laxmi carries out a similar test with the same hypotheses, at the \(8 \%\) significance level, using another random sample of size 50 .
2. Given that the population mean is now 31.5, find the probability of a Type II error.
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