Chapter 7 Sec 2.2: Inference for Population Mean
In the previous chapter, you transitioned from categorical data to quantitative data. We started by looking at graphs and numerical characteristics of the distribution, and we found that looking at the variability of the distribution was often quite an important feature. With proportions, the sample proportion tells us everything about the shape, center, and variability of the sample distribution. But with quantitative data we will need to consider all three of these characteristics, as well as possible outliers and other unusual observations (e.g., clustering).
But often, like in Chapter 1, we want to make inferences beyond our sample data to a larger population or process. For example, in Investigation 5.1, you will explore whether the average healthy body temperature appears to now differ from 98.6 based on results from a large sample of individuals. To do this, we need to explore whether sample statistics (like the mean or median) follow a predictable pattern. The reasoning will be very similar to what you saw with sample proportions but we will need to consider a new probability model to take into account that we will also be estimating the variability in our quantitative variable.
