Fundamentally, we saw probability in the Statistics Lifecycle as the underlying tool required in order to ultimately produce inference about the population parameters. Why is it that we need probability? Why can't we go straight from using the sample to just applying those results directly to the population?

Because of the uncertainty generated by the use of a random sample.

Because we don't randomize in an observational study.

Because we can never generalize the sample to the population.

Because the sample is always unbiased.

You can go straight from using the sample to just applying those results directly to the population.