4 People who diet can expect to lose an average of 3 kg in a month. In a book, the authors claim that people who follow a new diet will lose an average of more than 3 kg in a month. The weight losses of the 180 people in a random sample who had followed the new diet for a month were noted. The mean was 3.3 kg and the standard deviation was 2.8 kg .

1. Test the authors' claim at the \(5 \%\) significance level, stating your null and alternative hypotheses.
2. State what is meant by a Type II error in words relating to the context of the test in part (i).