Random Sampling Distribution Test

An automobile manufacturer advertises that the meanpetrol 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 sampleof 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 testat 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.

** Please refer to the attachments for the complete solution **

Solution-Part-a:
STEP-1: Null and Alternate Hypothesis: (please see the attached file)
Null Hypothesis: The mean petrol consumption of the new hybrid car is greater than or equal to 4.6 litres per 100 km.
: (please see the attached file)
Alternate Hypothesis: The mean petrol consumption of the new hybrid car is less than 4.6 litres per 100 km.
: (please see the attached file)
STEP-2: Analysis Plan:
(please see …

In this solution we perform a hypothesis test and answer a series of questions associated with it.