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Module · 5 lessons
Statistical Inference
Draw trustworthy conclusions from samples — sampling distributions, confidence intervals, hypothesis testing, and chi-squared tests.
At a glance
Level
Intermediate
Lessons
5 lessons
Time to complete
1–2 weeks
Cost
Free forever · no sign-up
This is where everything comes together. You learned to describe data, then to reason about chance. Statistical inference combines the two to answer the question that motivates almost all of statistics: given only a sample, what can I say about the population — and how sure can I be?
You will begin with the sampling distribution, the idea that a statistic like the mean is itself a random variable with its own spread, and use it to build confidence intervals that put honest error bars on an estimate. Then you will learn hypothesis testing: a disciplined way to decide whether a pattern in your data is real or could easily be a fluke, using p-values and intuitive permutation tests. Finally you will meet the chi-squared test in its two forms — checking whether a distribution matches what you expected, and whether two categorical variables are related.
You will test real claims on real data: whether Japanese and American cars truly differ in fuel economy, or whether that gap could be chance; whether penguin species are spread evenly; whether where a penguin lives is related to what species it is. By the end you will be able to look at a result and answer the question every analyst is ultimately paid to answer — is this real?
Start with Lesson 1 and the concept that makes all of inference possible: the sampling distribution.
Lessons in this module
1
Sampling Distributions and Confidence Intervals
See why a sample statistic is itself random, learn the standard error and the Central Limit Theorem, and build confidence intervals two ways.
2
Hypothesis Testing
Learn the logic of hypothesis testing — null and alternative hypotheses, test statistics, p-values, and significance — by running a permutation test on real car data.
3
Chi-Squared Goodness of Fit
Test whether a categorical variable follows an expected distribution using the chi-squared goodness-of-fit test, by hand and with scipy.
4
Chi-Squared Test of Independence
Test whether two categorical variables are related using contingency tables, expected counts, and the chi-squared statistic in Python.
5
Guided Project: Do Japanese and American Cars Really Differ?
The course capstone: use the full inference toolkit — confidence intervals, a permutation test, a t-test, effect size, and a chi-squared test — to settle whether 1970s-80s Japanese and American cars genuinely differed.
Achievement
Complete all 5 lessons to finish the Statistical Inference module.