2 Inferential statistics

From the previous section, we know that in our sample, the men were taller, on average, than the women: \(\bar{x}_{men}= 176.4 > \bar{x}_{women}= 165.8\). However, we are not only interested in the men and women in our sample, but want to answer a question about the population: In general, are men taller, on average, than women? Using mathematical notation, this question becomes: \(\mu_{men}> \mu_{women}\) or \(\mu_{men} - \mu_{women}> 0\). We use Greek letters to represent statistics at the population level; the Greek letter \(\mu\) represents the mean of the population.

We will formulate an answer to the question about the population means, based on the data in our sample. However, let’s first explore how height is distributed in the populations of men and women. Afterwards, we will discuss how population distributions determine what kind of samples we are likely to observe.