2 The times taken for the pupils in Ming's year group to do their English homework have a normal distribution with standard deviation 15.7 minutes. A teacher estimates that the mean time is 42 minutes. The times taken by a random sample of 3 students from the year group were 27, 35 and 43 minutes. Carry out a hypothesis test at the \(10 \%\) significance level to determine whether the teacher's estimate for the mean should be accepted, stating the null and alternative hypotheses.