Module 3 Confidence intervals and hypothesis testing

Module overview: statistical inference with NOAA summaries (90%, 95%, and 99% confidence intervals); tests of climate-related claims using \(p\)-values and critical values; interpreting significance and uncertainty in applied language.

3.1 Data source

Combine U.S. Climate Normals (1991 to 2020) with recent GHCN-Daily observations for the same location so students compare recent conditions to published normals.

Core variables: monthly or daily temperature and precipitation summaries (as appropriate to your download)
Normals: NOAA U.S. Climate Normals
Recent data: GHCN-Daily

3.2 Statistics topics

Confidence intervals at 90%, 95%, and 99%
Null and alternative hypotheses for concrete climate questions
Test statistics, critical values, and \(p\)-values
Type I and Type II errors in plain language

3.3 Suggested workflow

Download normals and a recent sample for the same location.
Construct at least one 95% confidence interval.
Run one hypothesis test against the normal reference value.
Explain the \(p\)-value in non-jargon terms.
Show the expected format for a short inference write-up.

3.4 Assignment

Replicate the instructor inference walkthrough using NOAA data.

2 Sampling variation, Monte Carlo simulation, and the Central Limit Theorem

4 Simple linear regression