Discussion:
An automobile manufacturer advertises that the mean petrol consumption of its new hybrid car does not exceed 4.6 litres per 100 km. An independent company decides to test the manufacturer's claim by selecting a random sample of 16 vehicles and measuring the consumption of each. They have found that the petrol consumptions in litres per 100 km of those vehicles are as follows:
4.7 4.9 4.4 4.5 4.6 4.7 4.7 4.8 4.9 4.3 5.0 4.6 4.7 4.9 4.8 5.1
a) Perform a hypothesis test at the 5% level to see if there is evidence to support the manufacturer's claim.
b) State the distributional assumption required for the test in part (a) to be valid, and use an appropriate plot to test the assumption. With reference to your plot, briefly explain why the assumption is or is not satisfied.
c) Based on your answers to parts a) and b), should the manufacturer be reported to a fair trading commission for misleading advertising? Briefly explain your decision.