Week 12 — Readings & Resources · Confidence Intervals for Proportions

Course: Introduction to Statistics (MATH 11) · Silver Oak University (fictional sample) · Prof. Rivera
Objective covered: Objective 6 — Construct and interpret confidence intervals for proportions.

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's load is deliberately light: ~4 short readings + ~3 short videos, grouped by the ideas 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 45–55 minutes if you do everything, far less if you pick one per group.

Reading order that matches the lecture: ① the one-proportion z-interval (and when you're allowed to use it) → ② constructing the interval & where z* comes from → ③ the margin of error and choosing a sample size → ④ interpreting the interval correctly (and the misinterpretations).

A habit to keep: our course supplies every z* value — you never look one up (90% → 1.645, 95% → 1.960, 99% → 2.576). As you read, focus on the ideas (why the margin is widest near 50%, what "95% confident" really means, why pollsters plan for the worst case), not on memorizing tables.

① The One-Proportion z-Interval (and its conditions)

Maps to Lecture Segments 2 & 5. A proportion uses z* (no degrees of freedom — that was last week's t-interval for a mean), and it's only trustworthy when three conditions hold: random, independent, and large counts (n·p̂ ≥ 10 and n(1−p̂) ≥ 10).

Reading — "Understanding Confidence Intervals: Easy Examples & Formulas" (Scribbr)
🔗 https://www.scribbr.com/statistics/confidence-interval/
Why it's assigned: the cleanest plain-language overview of what a confidence interval is and how to build one — and it explicitly covers the proportion case (using p̂(1−p̂) in place of a standard deviation), which is exactly our week. Skim the means part; focus on the proportion example.
⏱ ~8 min

Reference — "Conditions for Inference on a Proportion" (Khan Academy, article)
🔗 https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/one-sample-z-interval-proportion/a/conditions-inference-one-proportion
Why it's here: a one-page checklist of the three conditions we used in class — random, independent (10% rule), and the large-counts / success–failure rule (≥ 10 expected successes and ≥ 10 failures). Read it once so the "can I even do this?" step becomes automatic.
⏱ ~5 min

② Constructing the Interval — and Where z* Comes From

Maps to Lecture Segments 2–3. The whole formula in words: "sample percentage, give or take z* times the standard error," i.e. p̂ ± z*·√(p̂(1−p̂)/n).

Video — "Confidence interval example" (Khan Academy, AP Statistics)
🔗 https://www.khanacademy.org/math/statistics-probability/confidence-intervals-one-sample/estimating-population-proportion/v/confidence-interval-example
Why it earns the click: a quick, fully worked example of building a confidence interval for a proportion from a sample — the same four-step move (SE → z* → margin → endpoints) we did in Segment 2.
⏱ ~7 min

Video — "Critical value (z*) for a given confidence level" (Khan Academy, AP Statistics)
🔗 https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/one-sample-z-interval-proportion/v/critical-value-for-a-given-confidence-level
Why it's here: shows where the z* numbers in our embedded table (1.645, 1.960, 2.576) come from. You won't need to look one up for any of our problems — we supply the value — but it helps to see the source once (and why 95% lands on ≈ 1.96).
⏱ ~5 min

③ The Margin of Error & Choosing a Sample Size

Maps to Lecture Segments 3–4. The margin of error is the "±" the news reports: ME = z*·√(p̂(1−p̂)/n). Flip it around and you get the pollster's tool: n = (z*/ME)²·p̂(1−p̂), using the worst-case p̂ = 0.5 when you have no estimate.

Video — "Determining sample size based on confidence and margin of error" (Khan Academy, AP Statistics)
🔗 https://www.youtube.com/watch?v=VyFs7fsWE6w
Why it earns the click: the single best short walk-through of solving for n to hit a target margin — including why you plug in p̂ = 0.5 for the conservative worst case and round up. This is Segment 4 in video form.
⏱ ~6 min

Video — "Understanding and calculating confidence intervals for population proportions" (Dr Nic's Maths and Stats)
🔗 https://www.youtube.com/watch?v=OkR3PkT15uM
Why it earns the click: a lively, plain-English tour that ties the margin of error to the interval's width and to the confidence level using real polling examples (the "±4 points" headline) — and connects directly to how the sample size drives that margin.
⏱ ~7 min

④ Interpreting a Proportion Interval Correctly (and the Misinterpretations)

Maps to Lecture Segment 6. The line to carry out of this week: "95% confident" describes the method over many samples — not the people, and not the odds for this one interval.

Video — "Top Tips for How to Construct a Confidence Interval for a Population Proportion [AP Statistics]" (Michael Porinchak)
🔗 https://www.youtube.com/watch?v=xVam_IGwR8w
Why it earns the click: walks the full build and the correct interpretation for a proportion, calling out the classic mistakes — exactly the "build it, then say what it means without overclaiming" arc we did in class. A clean end-to-end model.
⏱ ~10 min

Reading — "What Is Standard Error? How to Calculate" (Scribbr)
🔗 https://www.scribbr.com/statistics/standard-error/
Why it's assigned: the standard error is the engine inside the margin of error. This short page makes SE concrete — why dividing by √n shrinks it, and how it differs for a proportion vs. a mean — so "√(p̂(1−p̂)/n)" stops looking like a mystery.
⏱ ~6 min

Optional one-stop reference (free online text)

If you'd like one optional reference to skim, OpenIntro Statistics keeps its full text and per-section videos free to read online. For proportions, see Section 5.2 ("Confidence intervals") — taught using a proportion — and Chapter 6 ("Inference for Categorical Data"), Section 6.1 ("Inference for a single proportion"), which includes the conditions and the sample-size idea.
🔗 https://www.openintro.org/book/os/
Why it's here: a reputable, currently-available reference you can return to in later weeks — entirely optional this week.

Pick-one quick path (≈15 min total)

In a hurry? Do exactly these and you'll be ready for the quiz:
1. Read Understanding Confidence Intervals (group ①) — focus on the proportion example.
2. Watch Confidence interval example (group ②) — the four-step build for a proportion.
3. Watch Determining sample size based on confidence and margin of error (group ③).
4. Watch Top Tips for How to Construct a CI for a Population Proportion (group ④) — build + interpretation.

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