An organisation wants to estimate the actual electricity usage of a refrigerators that has an advertised energy usage of 439. 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.
(a) Do you think that the 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.