Unit 4 Hypothesis Testing: One Sample

In the previous unit we learned that every estimate comes with uncertainty. A confidence interval tells us which population values are plausible given our sample.

But many real statistical questions begin with a specific claim. Has average monsoon rainfall changed? Is the unemployment rate below 5%? Does a new drug lower blood pressure?

Rather than asking which values are plausible, these questions ask is this particular claim consistent with the data? Answering that is the purpose of hypothesis testing.

Consider a claim made about a population. You collect a sample. Your estimate is not exactly what the claim predicted.

Should you conclude that the claim is wrong?

Or is this simply the kind of difference that appears because every random sample is slightly different?

That question is the starting point for hypothesis testing, and it is the engine behind much of modern statistics.