(3) [H] (8 marks) Many scientists are concerned about changes in the ice thickness due to global warming. Suppose the historical mean thickness of the ice just off the coast of Barrow, Alaska, is 3.32 meters. A recent random sample (n = 28) of the ice thickness near Barrow was obtained. The sample mean ice thickness is 4.036 meters. Assume a = 2.8 meters, and the underyling distribution is normal. Conduct a hypothesis test to determine whether there is any change in the mean ice thickness. (4) [H] Manatees are one creature found in coastal waterways. 10 years ago, researchers concluded that the true mean weight of manatees was approximately 1050 lbs. This year, a random sample of 12 manatees were selected, the sample weights are: 956, 1012, 954, 988, 973, 1048, 1075, 1064, 856, 1026, 1031, 1064. Assume the underlying distribution of manatee weights is normal, and population standard deviation 0 is unknown. (a) (8 marks) Implement a hypothesis test to verify if there is any evidence to suggest the true mean weight decreases now. (b) (4 marks) Use the given sample data to calculate 90% confidence interval for current mean weight of manatees