, which is a function of the data, to approximate the true value of

The final pillar of our lecture is hypothesis testing. This is the formal procedure for deciding between two competing claims: the null hypothesis and the alternative hypothesis. We use a test statistic to determine if the observed data is sufficiently extreme to warrant rejecting the null hypothesis. This process involves a delicate balance between Type I errors (false positives) and Type II errors (false negatives). The p-value, perhaps the most famous metric in statistics, tells us the probability of obtaining results at least as extreme as the ones observed, assuming the null hypothesis is true.

: Involves estimating the value of a population parameter.

A random variable is a variable whose possible values are numerical outcomes of a random phenomenon. There are two types:

Once probability is mastered, the lecture turns to the art of guessing.