Is a population proportion equal to 0.8, or is it lower?
Consider a random sample of n = 100 values from a population in which it is claimed that the probability of success is at least 0.80.
Is an observed count of x = 72 successes low enough to throw doubt on the claimed probability of success, 0.80?
Simulation
We can perform a simulation with probability 0.80 of success to generate a random sample 100 successes and failures. The diagram below shows the numbers of successes in 200 such simulations.
If the probability of success was really 0.80, there would be approximately 10/200 = 5% chance of 72 or successes being observed. Since this is low,
There is moderately strong evidence that the probability of success is less than 0.80 — observing only 72 successes would be unlikely if the probability really was 0.80.