Week 14 — Readings & Resources · Tests for Means & Proportions

Course: Introduction to Statistics (MATH 11) · Silver Oak University (fictional sample) · Prof. Rivera
Objective covered: Objective 7 — Conduct and interpret hypothesis tests for means and proportions (this week: the mechanics — the one-sample t-test, the two-sample idea, and the one-proportion z-test).

How to use this page

Everything here is a link to an external resource — open it in your browser, the same way you'd open a YouTube link. Nothing needs to be downloaded.

This week we turn last week's logic into real tests, so the readings are grouped by the three tools from the lecture. Read or watch one item per group and you're ready for the quiz; do all of them and you'll be very comfortable. Total time is roughly 45–60 minutes if you do everything, far less if you pick one per group.

Reading order that matches the lecture: ① the one-sample t-test for a mean → ② the two-sample comparison of means (conceptual) → ③ the one-proportion z-test → ④ a quick refresher on the test statistic / standard error that all three share.

A habit to start now: before you run any test, ask the week's two questions — Is this about a mean or a proportion? One group vs. a number, or two groups vs. each other? That picks the test every time. Keep it in mind as you read.

① The One-Sample t-Test (a claim about one mean)

Maps to Lecture Segments 2–4. The skill: State → Compute t = (x̄ − μ₀)/(s/√n) → Compare p to α → Conclude in context. The denominator is the standard error s/√n — don't drop the √n.

Reading — "An Introduction to t Tests | Definitions, Formula and Examples" (Scribbr)
🔗 https://www.scribbr.com/statistics/t-test/
Why it's assigned: the clearest plain-language walkthrough of the t-test — what it is, the one-sample formula, when to use it, and how to read the result. (It also covers the two-sample / independent t-test in the same article, which sets up group ②.) Read the one-sample section for this week.
⏱ ~9 min

Reading — "Significance tests (hypothesis testing)" (Khan Academy, unit)
🔗 https://www.khanacademy.org/math/statistics-probability/significance-tests-one-sample
Why it's assigned: Khan's one-sample inference unit bundles the t-test for a mean and the test for a proportion (group ③) in one place, with short worked videos and practice. A great one-stop hub for both one-sample tools this week.
⏱ ~8 min (pick the "test about a mean" lesson)

Video — "Test Statistics: Crash Course Statistics #26"
🔗 https://www.youtube.com/watch?v=QZ7kgmhdIwA
Why it earns the click: the liveliest tour of what a test statistic is and how t- and z-statistics turn a sample into evidence — exactly the Segment-3 idea of "distance ÷ wobble."
⏱ ~12 min

② The Two-Sample Comparison (two group means — conceptual)

Maps to Lecture Segment 6. This week you interpret a two-sample result, you don't compute it by hand. The question changes from "one group vs. a number" to "are these two groups different from each other?" (H₀: the two means are equal).

Reading — "Inference comparing two groups (two-sample)" (Khan Academy, unit)
🔗 https://www.khanacademy.org/math/statistics-probability/significance-tests-confidence-intervals-two-samples
Why it's assigned: the cleanest introduction to comparing two means — what the hypotheses look like (equal vs. different) and how to read the conclusion. Skim the overview; the conceptual picture is all you need this week.
⏱ ~7 min

Video — "T-Tests: A Matched Pair Made in Heaven: Crash Course Statistics #27"
🔗 https://www.youtube.com/watch?v=AGh66ZPpOSQ
Why it earns the click: builds up the two-sample / paired t-test with real examples — the perfect concrete picture of "comparing two groups" before you interpret one in the discussion.
⏱ ~11 min

③ The One-Proportion z-Test (a claim about one percentage)

Maps to Lecture Segment 5. The skill: State → Compute z = (p̂ − p₀)/√(p₀(1−p₀)/n) → Compare p to α → Conclude. The standard error uses p₀ (the null value), and proportions go in as decimals.

Reading — "Hypothesis Testing | A Step-by-Step Guide with Easy Examples" (Scribbr)
🔗 https://www.scribbr.com/statistics/hypothesis-testing/
Why it's assigned: the same clean five-step pipeline we use all week — state the hypotheses, compute the statistic, compare to α, conclude — applied to test claims including proportions. The structure maps one-to-one onto the z-test pipeline from Segment 5.
⏱ ~8 min

Video — "Test for a population proportion (large sample)" (Khan Academy)
🔗 https://www.khanacademy.org/math/statistics-probability/significance-tests-one-sample/more-significance-testing-videos/v/large-sample-proportion-hypothesis-testing
Why it earns the click: a short, worked one-proportion z-test — sets up p₀, builds the standard error, computes z, and reads the decision. Exactly the Segment-5 example, done on screen.
⏱ ~10 min

④ The Engine Under All Three — Test Statistic & Standard Error

Maps to Lecture Segments 2, 5, and the technology demo. Every test this week is distance ÷ wobble. The "wobble" is the standard error; the "distance ÷ wobble" is the test statistic.

Reading — "Test statistics | Definition, Interpretation, and Examples" (Scribbr)
🔗 https://www.scribbr.com/statistics/test-statistic/
Why it's assigned: ties the whole week together — what a test statistic is, how t and z versions are built, and how a bigger statistic means more surprising data (smaller p). A good capstone after the three tools.
⏱ ~7 min

Video — "Standard Deviation vs Standard Error, Clearly Explained!!!" (StatQuest with Josh Starmer)
🔗 https://www.youtube.com/watch?v=A82brFpdr9g
Why it earns the click: the standard error is the denominator in every formula this week, and students constantly confuse it with the standard deviation. This clears it up in one friendly, visual pass.
⏱ ~5 min

Video (optional) — "p-values: What they are and how to interpret them" (StatQuest with Josh Starmer)
🔗 https://www.youtube.com/watch?v=vemZtEM63GY
Why it's here: once you've computed a t or z, you still compare its p-value to α — this is the careful, visual refresher on what that p-value means (and the misreadings to avoid), carried over from Week 13.
⏱ ~11 min

Optional one-stop reference (free online text)

If you'd like one optional reference to skim, OpenIntro Statistics keeps its full text free to read online. Chapter 7 ("Inference for Numerical Data") covers the one-mean t-test and the difference of two means, and Chapter 6 ("Inference for Categorical Data") covers the one-proportion z-test — everything in this week, with worked examples.
🔗 https://www.openintro.org/book/os/
Why it's here: a reputable, currently-available reference you can return to for Week 15 — entirely optional this week.

Pick-one quick path (≈18 min total)

In a hurry? Do exactly these four and you'll be ready for the quiz:
1. Read the one-sample section of "An Introduction to t Tests" (group ①).
2. Watch Khan — "Test for a population proportion" (group ③).
3. Skim the two-sample Khan overview (group ②) for the equal-vs-different picture.
4. Watch StatQuest — "Standard Deviation vs Standard Error" (group ④).

Heads-up (links rot): these point to outside sites and YouTube channels that occasionally move, rename, or remove pages. If a link ever fails, tell Prof. Rivera and use the OpenIntro reference above in the meantime.