4 In the past the time, in minutes, taken by students to complete a certain challenge had mean 25.5 and standard deviation 5.2. A new challenge is devised and it is expected that students will take, on average, less than 25.5 minutes to complete this challenge. A random sample of 40 students is chosen and their mean time for the new challenge is found to be 23.7 minutes.

1. Assuming that the standard deviation of the time for the new challenge is 5.2 minutes, test at the \(1 \%\) significance level whether the population mean time for the new challenge is less than 25.5 minutes.
2. State, with a reason, whether it is possible that a Type I error was made in the test in part (a).