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, yielding the data below in kg: {213029, 18.1272, 19.7044, 22.1150, 10.3000, 23.0314, 22.9403, 23.1920... 20.2311, 19.7303} Throughout this question you should assume a Gaussian model for the data. (a) Write down the data likelihood function dening all variables you use, and hence calcu- late the maximum likelihood estimator {MLE} for the population mean and variance. How does the sample variance compared to the MILE estimator for the variance in this particular case? [b] Assume that the true standard deviation is {as claimed by the sender] is 2000 g and perform a hypothais test regarding the claim that the average sack weight is 20 kg using the above data at a level of signicance ct = 0.05 and compute the p value of the test. Further compute the power of the test if the true mean is it] = 22. (e) The vendor claims that the standard deviation in the weight of the sacks is less than 2 kg. Construct an appropriate condence interval at condence level 1 ct = 0.95 for the variance and test the vendor's claim