Does transmitted sound of killer whale scare whales?

Even with no sound, 40% of whales leave immediately.

When the sound was used, 15 out of 30 left immediately.


X   ~   binomial (n = 30, π)

H0:   π = 0.4        HA:   π > 0.4

A simulation was used earlier to find the approximate p-value for this test by generating repeated samples from a population with π = 0.4. This page illustrates that the binomial distribution can give the p-value directly without simulation.

The p-value is a sum of binomial probabilities

Firstly repeat the simulation — click Accumulate then hold down Simulate until about 100 samples of 30 whales have been generated. This gives an approximation to the p-value.

Now select Binomial distribution from the pop-up menu. The exact probability of getting 15 or more whales to leave immediately is 0.1754 if π = 0.4. This is the p-value for the test.

The conclusion is the same as before:

There is probability 0.1754 that 15 or more whales are scared off even if the device is ineffective so the data provides no evidence that the device is effective.


In 1987, the Federal Aviation Administration (FAA) investigated security at Los Angeles International Airport (LAX). In one test, it was found that only 72 out of 100 mock weapons that FAA inspectors tried to carry onto planes were detected by security guards (Gainesbille Sun, Dec 11, 1987).