Section 2d - Project on simulation
Exploration
In this case I will be using simulation to explore a situation rather than trying to
answer a particular question. I will be simulating the gender of the driver in an
OPP random check of 100 vehicles (not including large truck etc. which require
special driver's license) on the 401 for a given day of the year. I aim to explore
how the composition of these samples can vary when the procedure is repeated.
I will look at the proportion of male drivers in each sample and the mean and
standard deviation of the data accumulated when the experiment is repeated.
Plan
As an estimate of the probability of the driver of the car being male or female
I used the data provided by the Ontario Ministry of Transport in its 2000
Ontario Road Safety Annual Report, Table 2.16 which provides Sex of Driver
Population by Age Groups 2000. As part of the simulation I will assume that
only Ontario drivers will be stopped.
Analysis
From Table 2.16 of the report 2000 Ontario Road Safety Annual Report I find
that there are 4,313,694 male drivers out of a total of 8,121,374 licensed
Ontario drivers. Thus the probability that a random licensed Ontario driver
is male is 0.531 (to three decimal places).
Since this is a two outcome experiment and if I assume that drivers are
statistically independent the experiment suggests a Binomial Probability model.
So, with a sample of 100 vehicles, the mean number of males driving the cars
is given by
µ = np or µ = 53.1 males, with a standard deviation of
However this does not provide me with an indication of what could be the result in each sample. To get this view I tried a simulation and to do this I followed the Instructions given in a Fathom Workshop Guide (reference)
The results of the simulation follow:I introduced a slider for the probability of stopping a male driver and set it to as
close to 0.531 as I could
Through the simulation I generated a table of the sample data
from which I generated a Bar Chart of the gender distribution for 100 drivers.
A typical distribution was
I then repeated the simulation 200 times, in each case, noting the mean proportion of male drivers in each sample. These 200 data were then plotted in a bar chart
and the mean and standard deviation of this distribution was calculated
Observations
Through the simulation I saw that the sample composition of male and female
drivers could change quite a bit from sample to sample, not only in terms of totals
but also in the order in which they appeared. When this process was repeated a
large number of times, the mean proportion of all the samples was close to the
one on which I based my simulation, and although this number changed slightly
as the number of repetitions was increased, it stayed consistently close to 0.531,
which I noticed it is µ/n (where µ is the mean of the Binomial distribution). The
behaviour of the standard deviation was a bit more erratic than that of the mean
but it did move around the value of 0.05. I explored to see whether this was
related to any of the values that I used in the simulation. I found that it is close to
the sqrt(.431x.469) and is therefore also close to ó/sqrt(n) (where ó is the
standard deviation of the Binomial distribution).
