A shipment of 1000 sacks of oranges arrives at a distribution centre in Edinburgh, one of 10 such facilities in Scotland. The sender quotes a nominal weight of 20 kg and a standard deviation of no more than 2000 g per sack. A random sample of 10 sacks is selected and weighed, giving a mean of = 20.77 kg and variance S2 4.85 kg2. Throughout this exercise you should assume a Gaussian model for the data. = (b) Assume that the true standard deviation is (as claimed by the sender) is 2000 g and perform a hypothesis test regarding the claim that the average sack weight is 20 kg using the above data at a level of significance a = 0.05 and compute the appropriate p-value. You may assume that most of the imported oranges in Scotland arrive through this specific distribution centre. Further compute the power of the test if the true mean is given by ₁ = 22.