A shipment of 1000 boxes of pens arrives at a distribution centre. The sender quotes a nominal weight of 20 kg and a standard deviation of no more than 2000 g per box. A random sample of 10 boxes is selected and weighed, yielding the data below in kg: {21.7629, 18.1272, 19.7044, 22.1150, 16.8006, 23.0314, 22.9463, 23.1920, 20.2317, 19.7803} Throughout this question you should assume
A shipment of 1000 boxes of pens arrives at a distribution centre. The sender quotes a nominal weight of 20 kg and a standard deviation of no more than 2000 g per box. A random sample of 10 boxes is selected and
weighed, yielding the data below in kg:
{21.7629, 18.1272, 19.7044, 22.1150, 16.8006, 23.0314, 22.9463, 23.1920, 20.2317, 19.7803}
Throughout this question you should assume a Gaussian model for the data.
(a) Write down the data likelihood
How does the sample variance compared to the MLE 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 hypothesis test regarding the claim that the average box weight is 20 kg using the above data at a level of significance α = 0.05 and compute the p value of the test. Further compute the power of the test if the true mean is µ1 = 22.
(c) The vendor claims that the standard deviation in the weight of the boxes is less than 2kg. Construct an appropriate confidence interval at confidence level 1 − α = 0.95 for the variance and test the vendor’s claim
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