As a data analyst for the ACCC you have been asked to test claims that petrol bowsers (dispensers of petrol) of a particular petrol station chain are under-fuelling customers in a particular metropolitan area (i.e., the amount of fuel received is less than the number of litres displayed on the bowser as having been dispensed).

A random sample of 30 bowsers were considered across the metropolitan area. At each bowser, an ACCC member filled a 10 Litre can until the number of litres displayed on the bowser read as 5.00 Litres. The contents of the can were then measured.

The sample yielded a standard deviation of 0.11 Litres and a mean of 4.97 Litres.

a. Conduct a hypothesis test at the 5% significance level of whether the petrol station appears to be under-fuelling customers. What are the steps excluding the test of the assumptions which you can assume hold true.

b. Considering the sample mean was less than 5 Litres, how can you explain the result of your hypothesis test?

c. Assuming the sample standard deviation is essentially equal to the population standard deviation (i.e., that it wouldn't change amongst different samples), how could the design of the sample be modified to produce a different result from the hypothesis test to what you found?