Week 11 — Readings & Resources · Confidence Intervals for Means

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

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 four 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 t-distribution (why t, not z; degrees of freedom) → ② constructing a confidence interval for a mean → ③ the margin of error → ④ interpreting the interval correctly (and the misinterpretations).

A habit to keep: our course supplies every t* value — you never look one up. As you read, focus on the ideas (why the interval is wider for small samples, what "95% confident" really means), not on memorizing tables.

① The t-Distribution · Why t, Not z? · Degrees of Freedom

Maps to Lecture Segment 2. The punchline: with σ unknown you use t (df = n − 1), which is a little wider than z — and slides toward z as the sample grows.

Reading — "T-Distribution: What It Is and How To Use It (With Examples)" (Scribbr)
🔗 https://www.scribbr.com/statistics/t-distribution/
Why it's assigned: the cleanest plain-language version of exactly what we did in class — why small samples and an unknown variance push you from z to t, how degrees of freedom (n − 1) pick the curve, and how the t-distribution closes in on the z-distribution as df grows.
⏱ ~7 min

Reference — "Student's t Table — Guide & Examples" (Scribbr)
🔗 https://www.scribbr.com/statistics/students-t-table/
Why it's here: shows where t* critical values come from, so the numbers in our embedded table (2.262, 2.131, 2.064, 1.960 …) aren't a mystery. You won't need to read a table for any of our problems — we supply the value — but it helps to see the source once.
⏱ ~5 min

② Constructing a Confidence Interval for a Mean

Maps to Lecture Segments 3–4. The whole formula in words: "sample mean, give or take t* times the standard error," i.e. x̄ ± t*·(s/√n).

Reading — "Confidence Interval: How to Calculate It + Examples" (Scribbr)
🔗 https://www.scribbr.com/statistics/confidence-interval/
Why it's assigned: walks the build step by step — point estimate, standard error, critical value, margin of error, endpoints — the same four-step recipe from the lecture, with worked numbers you can follow.
⏱ ~8 min

Video — "T-statistic confidence interval" (Khan Academy, AP Statistics)
🔗 https://www.khanacademy.org/math/statistics-probability/confidence-intervals-one-sample/estimating-population-mean/v/t-statistic-confidence-interval
Why it earns the click: a quick worked example of building a confidence interval for a mean using the t statistic when σ is unknown — exactly the move in Segment 3.
⏱ ~6 min

③ The Margin of Error

Maps to Lecture Segment 4. The margin of error is the "±" the news reports: ME = t*·(s/√n) — bigger n shrinks it, more spread or more confidence grows it.

Video — "Confidence intervals and margin of error" (Khan Academy, AP Statistics)
🔗 https://www.youtube.com/watch?v=hlM7zdf7zwU
Why it earns the click: connects the margin of error to the interval's width and to the confidence level, with the polling examples (the "±3 points" headline) we opened the week on.
⏱ ~5 min

④ Interpreting a Confidence Interval Correctly (and the Misinterpretations)

Maps to Lecture Segment 5. The line to carry out of this week: "95% confident" describes the method over many samples — not the data, and not the odds for this one interval.

Reading — "Interpreting a Confidence Interval for a Mean" (Khan Academy, article)
🔗 https://www.khanacademy.org/math/statistics-probability/confidence-intervals-one-sample/estimating-population-mean/a/interpret-one-sample-t-interval-mean
Why it's assigned: the single best short page on the correct interpretation and the exact misreadings we banned in class — "95% of the data" and "95% chance the true mean is in this interval." Read this one twice.
⏱ ~6 min

Video — "Confidence Intervals: Crash Course Statistics #20"
🔗 https://www.youtube.com/watch?v=yDEvXB6ApWc
Why it earns the click: the liveliest tour of what a confidence interval means — the long-run "95 of 100 intervals capture the truth" picture — with real examples (delivery windows, election margins) that make the interpretation stick.
⏱ ~12 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. Chapter 7 ("Inference for Numerical Data") covers everything in this week — the t-distribution (7.1A) and inference for one mean (7.1B), including confidence intervals.
🔗 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 T-Distribution (group ①) — why t, not z.
2. Read Confidence Interval: How to Calculate It (group ②) — the four-step build.
3. Watch Confidence intervals and margin of error (group ③).
4. Read Interpreting a Confidence Interval for a Mean (group ④) — the two misinterpretations.

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.