2. A researcher believes that the mean weight loss of those people using a slimming plan as part of a group is more than 1.5 kg a year greater than the mean weight loss of those using the plan on their own. The mean weight loss of a random sample of 80 people using the plan as part of a group is 8.7 kg with a standard deviation of 2.1 kg . The mean weight loss of a random sample of 65 people using the plan on their own is 6.6 kg with a standard deviation of 1.4 kg .

1. Stating your hypotheses clearly, test the researcher's claim. Use a \(1 \%\) level of significance.
2. For the test in part (a), state whether or not it is necessary to assume that the weight loss of a person using this plan has a normal distribution. Give a reason for your answer.