Final answer:
The rise of a penicillin-resistant strain of bacteria in patients is an example of evolution by natural selection, as the resistant bacteria survive antibiotic treatment and reproduce.
Step-by-step explanation:
The scenario where a penicillin-resistant strain of bacteria arises in hospitalized patients who do not complete the prescribed course of antibiotics is a clear example of evolution by natural selection. In the given context, the bacteria population already contains some individuals with the genetic mutation that confers resistance to penicillin.
When antibiotics are applied, those without the resistance die, while those with the resistance survive and reproduce, leading to a population where resistance is common. This process of survival and reproduction of the bacteria due to the beneficial trait of antibiotic resistance highlights the principles of natural selection, where the environment — in this case, the application of penicillin — determines which individuals survive to pass on their genes.