A p-value without understanding is a dangerous number. Today you learn what hypothesis testing actually asks, what p-values mean and don't mean, when to use t-tests versus chi-square tests, and how to avoid the most common statistical mistakes in practice.
By the end of this lesson you will formulate null and alternative hypotheses, run a two-sample t-test in Python, compute and interpret a p-value correctly, run a chi-square test for independence, and explain Type I and Type II errors with concrete consequences.
null hypothesis is the foundation of Day 3. Every concept that follows builds on the mental model you establish here. The most effective approach is to understand the principle first, then apply it — skipping straight to implementation creates gaps that compound into confusion later.
Work through each example in this lesson sequentially. The concepts connect, and the order is deliberate. If something is unclear, slow down at that point rather than pushing past it — a ten-minute pause now saves hours of debugging later.
Understanding null hypothesis requires seeing it in motion. The code below is not a complete application — it is a minimal, working illustration of the key mechanism. Study the pattern, run it, break it deliberately, then fix it. That cycle builds real comprehension.
Once the basic pattern works, the logical next step is p-value. This is where the abstraction becomes useful — you move from understanding the mechanism to applying it to real problems. The transition is usually smaller than it feels. Most of the hard work happened in Section 1.
t-test completes today's picture. It is where null hypothesis and p-value converge into a pattern you can apply to novel problems. This integration step is often where the day's learning consolidates — if the earlier sections felt abstract, this one typically makes them click.
Implementing null hypothesis alone handles the happy path. Real systems encounter edge cases, invalid input, and unexpected state. Missing p-value means missing those guards.
Combining null hypothesis with p-value gives you a complete, defensible implementation. The extra lines cost ten minutes; the robustness they add is worth hours of debugging time.
Several mistakes appear consistently when engineers encounter Hypothesis Testing — Making Decisions with Data for the first time. Recognizing them now costs nothing; encountering them in production costs hours.
Two intensive days (Thu–Fri) with an instructor who has taught thousands of engineers. Cohorts in 5 cities, June–June–October 2026 (Thu–Fri).
Reserve Your Seat — $1,490Before moving on, you should be able to answer these without looking: