How long are bicycles hired for (on average) on the Santander London Bicycle Hire scheme?
A few years ago London introduced the Santander London Bicycle Hire scheme that gives people
the opportunity to hire bicycles from various docking stations in London. The scheme intends to
promote the use of bicycles in London as a way to reduce traffic, congestions and to improve
people’s fitness. The scheme is designed to favour the use of the bicycles for a short period of time,
usually less than 30 minutes. In fact, after paying the access fee of £2, the first 30 minutes of usage
are free and it costs £2 to hire the bike for each extra period of up to 30 minutes. More information
about the scheme can be found from the following website:
http://www.tfl.gov.uk/modes/cycling/santander-cycles/what-you-pay
Moreover, the “Queen Marys, Mile End” docking station has been available for only about one year
and transport for London believes that about 0.5% of all cycle journeys start or end at this station.
You are asked to use inferential statistics to 1) estimate the average length of bicycle hire and 2) to
estimate the proportion of journeys taking place from and to the “Queen Marys, Mile End” docking
station. To this end, on QMPlus you will be able to access the excel file “ECN121 Cycle Hire Data”
which contains a large amount of data about the actual usage of the bicycles during the month of
October 2014.
Complete the following tasks.
a) Provide a brief explanation of how you would organise and carry out your research. (10 marks)
b) Suggest two unbiased estimators and use them to provide an estimate of:
1) the average length of the bike hire; (10 marks)
2) the proportion of bike journeys taking place from and to the “Queen Marys, Mile End”
docking station. (10 marks)
c) Construct two confidence intervals that have a high probability of:
1) capturing the average length of the bike hire; (10 marks)
2) the actual proportion of bike rides taking place from and to the “Queen Marys, Mile End”
docking station. (10 marks)
d) Set up a hypothesis test to test whether the average length of the bike hire is consistent with
Transport for London expectation that the pricing scheme gives incentives to users to hire the
bikes for no longer than 30 minutes. (25 marks)
e) Set up a hypothesis test to test whether the proportion of bike rides taking place at the “Queen
Marys, Mile End” docking station is greater than the 0.5% expected by Transport for London.