4 In the past, the time taken by vehicles to drive along a particular stretch of road has had mean 12.4 minutes and standard deviation 2.1 minutes. Some new signs are installed and it is expected that the mean time will increase. In order to test whether this is the case, the mean time for a random sample of 50 vehicles is found. You may assume that the standard deviation is unchanged.

1. The mean time for the sample of 50 vehicles is found to be 12.9 minutes. Test at the \(2.5 \%\) significance level whether the population mean time has increased.
2. State what is meant by a Type II error in this context.
3. State what extra piece of information would be needed in order to find the probability of a Type II error.