17 The energy consumption of refrigerators sold in Australia and New Zealand is checked and appliances are given a star rating to guide consumers who...

8.17 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

consumption in kilowatts per annum is also displayed for each

model on the website 6www.energyrating.gov.au7. Suppose a

consumer organisation wants to estimate the actual electricity

usage of a model of refrigerator that has an advertised energy

usage of 439 kW per 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.

a. Assuming that the energy usage in the population is

normally distributed, construct a 95% confidence interval

estimate of the population mean energy usage for this

model of refrigerator.

b. Do you think that the consumer organisation should accuse

the manufacturer of producing fridges that do not meet the

advertised energy consumption? Explain.

c. Explain why an observed energy usage of 425 kW for a

particular refrigerator is not unusual, even though it is

outside the confidence interval developed in (a).