C) please Question 1A shipment of 1000 sacks of oranges arrives at a distribution centre in Edinburgh, one of10 such facilities in Scotland. The sender quotes a nominal weight of 20 kg and a standarddeviation of no more than 2000 g per sack. A random sample of 10 sacks is selected andweighed, giving a mean of x = 20.77 kg and variance S = 4.85 kg2. Throughout thisexercise you should assume a Gaussian model for the data.(a) Show that the sample mean coincides with the maximum likelihood estimator (MLE)for fl while the sample variance differs from the MLE for o2. Why is the MLE for thevariance not the preferred choice for small samples?(b) Assume that the true standard deviation is (as claimed by the sender) is 2000 g andperform a hypothesis test regarding the claim that the average sack weight is 20 kgusing the above data at a level of significance a = 0.05 and compute the appropriatep-value. You:may assume that most of the imported oranges in Scotland arrive throughthis specific distribution centre. Further compute the power of the test if the true meanis given by ₁ = 22.(c) The vendor claims that the standard deviation in the weight of the sacks is less than2 kg. Construct an appropriate confidence interval at confidence level 1-a = 0.95 forthe variance and test the vendor's claim.

A shipment of 1000 sacks of oranges arrives at a distribution centre in Edinburgh, one of 10 such…

Answered: (c) The vendor claims that the standard…

Linear Algebra: A Modern Introduction

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(c) The vendor claims that the standard deviation in the weight of the sacks is less than 2 kg. Construct an appropriate confidence interval at confidence level 1 - a = 0.95 for the variance and test the vendor's claim.