Initially, the population of bacteria was composed of mostly bacteria vulnerable to methicillin and a small number of resistant bacteria. Treatment with methicillin destroyed all of the vulnerable bacteria. leaving only the resistant alive to reproduce. Over time, the resistant bacteria became the majority.

Although it's possible a new patient could have introduced the first resistant bacteria, it's unlikely to have occurred in such a short time frame. 

It's also unlikely the bacteria possessed the ability to resist the bacteria from the start, as methicillin treatment wouldn't have worked on any of them.

Bacteria do not possess a mechanism by which they can build up immunity to antibiotics over time.

A sharp decrease in population size caused by environmental or human impact is known as the bottleneck effect, where the bottlenecking occurs in the relative population diversity. This is mainly due to the fact that the individuals who survived rarely represent the genetic makeup of the initial population as a whole. The effect size is a statistical measurement of the strength of a phenomenon, which can be applied in the study of population dynamics, but is not a type of genetic drift. Artificial selection is the deliberate selection of mating preferences by humans in order to alter the proportion of traits in the offspring. However, this type of selection is not caused by a dramatic event, nor does it result in a severe decrease in population size. The founder effect does pertain to small populations but specifically on how genetic variation is lost in a small population that comes from a larger population due to misrepresentation. 

This would be equivalent to the number of “grandchildren” produced by the organism. Biological fitness is defined by how capable the organism is of increasing the frequency of its own alleles. While individuals that consume more food grow larger, or have more mates than other members of their species are clearly thriving in their environment, which does not always mean that they produce more offspring. Also, it is possible that an organism could produce a large number of offspring that are infertile, which would ultimately not increase the frequency of its alleles. Therefore, the best determination of an organism’s fitness is the production of offspring that are themselves able to successfully produce offspring.

Selection pressures is the correct answer here. A selection pressure is any factor that affects fertility or mortality, or anything that can cause a population to change genetically.

Breeding with genetically different individuals tends to "scramble" the alleles of a population. When genetically similar individuals breed, they tend to produce homozygous genotypes in their offspring, so potentially dangerous recessive alleles appear more frequently and beneficial alleles are not as efficiently selected for. Thus, inbred populations have a lower survival rate over time. This is called inbreeding depression.

Each of the above is true, but the predictive power of evolution lies in its ability to form testable hypotheses. Natural selection and descent with modification can be most visibly observed in bacterial populations, where new generations can arise in as little as forty minutes. Biologists in every field form hypotheses based on how a mechanism, organism, or process is adaptive to its environment.

This is an example of a prediction made by the theory of natural selection.

There must have been individuals in the population who were already resistant to the antibiotic. They would survive while the non-resistant bacteria would die out, leaving only the resistant individuals to pass on their genes by multiplication.

The bacteria themselves do not grow resistant to the antibiotic, and they cannot change their genetic makeup in response to the environment.

Since the drug is an antibiotic, not a sterilization method, it will not succeed in killing the entire population of bacteria.

This principle is particularly important in the field of immunology, as biologists work to figure out how antibiotic-resistant strains can be fought or maintained.

While natural selection is often described as "survival of the fittest," this explanation is not completely accurate. It paints the picture that the most fit individual lives the longest, when the real premise is that the individual with the most benefical combination of genes suited to the current environment reproduces more, thus passing on more genetic information to the next generation.