Other uses of simulation
Simulations can help us to answer questions about a variety of other models (or populations). The following example shows another simple simulation.
Scaring whales from fishing boats
Commercial fishermen in some parts of the Atlantic Ocean occasionally have problems with whales scaring away fish. The whales often do not stay long, perhaps leaving to avoid the noise made by the boats. Sonar operators have found that 40% of all whales leave soon after the boat arrives.
In an attempt to get the whales to leave, an experiment was conducted in which a boat transmitted underwater the sounds of a killer whale. Of 30 whales, half were scared away immediately by this device. Since a higher proportion than 40% were scared away, can we conclude that the device is effective?
A simulation
If the device was ineffective, and every whale independently had probability 0.4 of leaving immediately, we know that the number scared away out of 30 whales will be a random quantity.
How unlikely is it to get as few as 15 out of 30 staying if the device is ineffective (and the probability of leaving is 0.4 is correct)?
A simulation helps to answer this question.
Click Simulate to randomly 'try the device on 30 whales', with each independently having probability 0.4 of leaving and 0.6 of staying — i.e. with the device having no effect. Click Accumulate then run the simulation between 100 and 200 times. (Hold down the Simulate button to speed up the process.)
Observe the distribution of the number of whales leaving. The proportion of simulations with 15 or whales leaving is shown to the right of the dot plot. Observe that this happens around 15% of the time.
We therefore cannot conclude that the device is effective — getting 15 whales leaving out of 30 is not unusual even if the device has no effect.
We will return to this example later.