1. Confidence

Thus far we have worried about two fundamental questions. In each case we have a sample of data from some universe or population, and we want to draw conclusions about the universe (population) from the sample.

Our questions are:

• Is our observed sample likely to be compatible with a null universe? This is statistical inference.
• Can we classify new data from the same universe using information from the sample — classification.

In this section we think about another common question that we ask about a sample — how close are measures from our sample likely to be the same measures from the universe or population?

We now enter the world of confidence intervals. We soon discover a tool called the bootstrap.