A supermarket in Newnham receives a shipment of 90 boxes of fresh salmon from a supplier in northern Tasmania. Before they accept the shipment, they randomly sample 9 boxes and after an inspection nd that 3 of them contain at least one defective salmon (which may imply the incorrect colour). a) Determine a 99% condence interval for the proportion of boxes in the shipment that contain at feast one defective salmon. [7 marks] b) The supermarket will accept a shipment unless they feel that there is a signicant risk that more than 10% of the boxes contain at least one defective salmon. Explain whether the supermarket should accept this shipment. [6 marks] c) The sample of 90 boxes of salmon has a mean weight of 497.3 grams, and a standard deviation of 4.8 grams. The supermarket will accept the shipment unless they have strong evidence that the shipment is underweight. Applying an alpha risk of o=1%, test the hypothesis that the mean weight of all boxes in the shipment is at least 500 grams. Expiain whether the supermarket should accept the shipment. [7 marks]