The energy consumption of refrigerators sold in Australia and New Zealand is checked and appliances are given a star rating to guide consumers who are about to make purchases. The energy consumption in kWh per annum is also displayed for each model on the website. Suppose a consumer organisation wants to estimate the actual electricity usage of a model of refrigerator that has an advertised energy usage of 439 kWh/annum. It tests a random sample of n = 18 fridges and finds a sample mean usage of 445 and a sample standard deviation of 40. Assume that the energy usage in the population is normally distributed. (You need to show all your calculations and demonstrate how you obtain your results).
(a) Do you think that the consumer organisation should accuse the manufacturer of producing fridges that do not meet the advertised energy consumption? You should justify your answer with a hypothesis test.
(b) Construct a 95% confidence interval estimate of the population mean energy usage for this model of refrigerator.
(c) Explain why an observed energy usage of 425 for a particular refrigerator is not an unusual value in the sample, even though it is outside the confidence interval developed in Part (b).