How to use this guide
Where this guide comes from. It follows the course's published description (probability with Bayes' law, expected values, discrete and continuous variables with the normal curve, graphs of data, and estimation by formula and by simulation) and the standard topics for an introductory statistics course. Instructors' emphasis and notation vary: check your own course outline.
The order. 01 to 05 build the toolkit: describing data, probability, random variables, the binomial and the normal. 06 to 08 are inference, where you use a sample to say something about a population: sampling distributions, confidence intervals (with a bootstrap lab) and a first look at hypothesis tests. Tab 08 is an introduction; some sections of the course cover it and some do not.
Inside a topic: read the idea, look at the formula, then open the worked example and follow every step. Close it and redo it on paper. Then change the numbers in the lab until the answer stops surprising you, and finish with the traps.
Notation used here: x̄ is a sample mean, μ a population mean, s a sample standard deviation, σ a population standard deviation, p̂ a sample proportion, p a population proportion, z a standardized value and t its small-sample cousin. Normal curves are written N(μ, σ) with the standard deviation second; some courses use the variance there instead.
Then practise. The Drill, the multiple-choice bank and the flashcards are all levelled:
| Level | What it asks | Example |
|---|---|---|
| Beginner | A definition, or one step: read one number or apply one formula | What is the z-score of 65 when μ = 50 and σ = 6? |
| Intermediate | A standard problem in a few steps | Find P(X < 490) for a normal variable and a binomial P(X = 6) |
| Exam level | A full exam-style question that strings several steps together | Build a 95% confidence interval for a mean with t and interpret it |
| Hard | Twists: topics combined, working backwards, and the traps that cost the most marks | Find the sample size that gives a margin of error of 2 |
The question generator starts on Auto: it begins at Beginner and moves up a level after three correct answers in a row. You can pick a level yourself at any time. The multiple-choice bank and flashcards are ordered from easy to hard, so working through them in order builds each idea from the ground up.
Normal areas in this guide are computed without a table, so labs and drills accept answers read from a standard z-table (z to 2 decimals) as long as they are within the stated rounding.
Exam format, weight and allowed aids differ between sections and terms. Check your own course outline.
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This is the first section. The full guide has every topic, the labs and the practice questions.
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