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Question 6 (15 marks) Marks a. A certain brand of milk powder is sold in packets with a mean weight of 2.5 kg. The brand has received complaints from customers that the weight is now less than 2.5 kg. As a result, the company randomly selects a sample of 60 packets and finds an average weight of 2.48 kg, with a sample standard deviation of 0.12 kg. At a 5% level of significance, carry out an appropriate hypothesis test to determine whether the weight is less than 2.5 kg. Assume that the weight of the milk powder is normally distributed. [5]Page 14 of 38 Question 6 (continued) Marks b . A researcher wants to see if a weight loss program is effective. He measures the weight of 8 randomly selected women before and after the weight loss program. Person Weight before Weight after d 1 78 69 2 82 71 3 76 78 4 81 73 5 76 69 6 78 67 7 69 58 8 73 65 Use this information to conduct a hypothesis test at a 5% level of significance to determine whether there is a significant difference in weight after the weight loss program. Assume that the weight loss of participants is normally distributed. [5]