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Teacher guide — Grade 11, Unit 3: Uncertainty: bootstrap and confidence intervals

Time: 3 lessons + project (about 5 periods). Track: B (code).

# Lesson Time
1 Sampling variation 40–45 min
2 The bootstrap 40–45 min
3 Interpreting intervals 40–45 min
P Unit project: How sure are we? 2 periods

Before you start

  • Materials: Notebook notebooks/bootstrap.ipynb; bag of numbered slips for the unplugged version.
  • Read docs/pedagogy/lesson-anatomy.md and docs/pedagogy/ai-use-policy.md.

If you have no computers / no internet

Write 20 values on slips, draw with replacement 20 times, compute the mean; repeat 10 times; plot the means.

Common misconceptions

  • A 95% interval means 95% of data lie inside it. It describes the uncertainty of the estimate.
  • Bootstrapping creates new information; it only reveals variability of this sample.

Differentiation

  • Support: give a partially filled table / sentence starters; pair with a data-steward role.
  • Stretch: ask "what would change your conclusion?" and "who is missing?"

Answer key (check questions)

Lesson 1: Sampling variation 1. Will two samples give the same mean?
Answer: Usually not. 2. Bigger sample → ?
Answer: Less variation in the estimate. 3. What causes the difference?
Answer: Chance in who ends up in each sample.

Lesson 2: The bootstrap 1. 'With replacement' means…
Answer: Each draw is put back, so items can repeat. 2. What do we compute each time?
Answer: The statistic (e.g. mean). 3. Middle 95% gives…
Answer: A 95% bootstrap interval.

Lesson 3: Interpreting intervals 1. Which is narrower, n=25 or n=400?
Answer: n = 400. 2. Does a narrow interval fix a biased sample?
Answer: No. 3. Is a 95% interval where 95% of the data lie?
Answer: No: it concerns the uncertainty of the estimate.

Assessment

Starter quiz each lesson (3 questions, one recalling the previous lesson); unit quiz in quiz.yml; project marked with the rubric in docs/pedagogy/assessment.md; 2-minute oral check per group.

Alignment

Enrichment aligned to NEB Grade 11–12 Computer Science (databases, programming) and Maths/Statistics.

Answers: practice exercises

  1. Parameter: the share of all Pokhara voters supporting the bus park (unknown). Statistic: 52% in the sample of 400.
  2. 8 ÷ √16 = 2 cm; 8 ÷ √64 = 1 cm.
  3. Without replacement, a resample of size n is just the same sample reordered; the statistic never changes. With replacement each resample is a different plausible sample.
  4. "Support is estimated at 48%; values from about 45% to 51% are consistent with the poll (sampling error only)." No: 50% is inside the interval, so a lead or a tie is possible — and non-sampling errors may be larger.
  5. n = 50 (random_state=3): mean 28.9, CI ≈ 26.7–31.1 (width ≈ 4.3 years); n = 200: mean 29.4, CI ≈ 28.3–30.5 (width ≈ 2.2) — about half, as expected for 4× data.
  6. 90% interval for n = 50: ≈ 27.1–30.7, narrower; less confidence needs a smaller range.
  7. Hill 0.421 (0.385–0.460, n = 696), Mountain 0.325 (0.248–0.395, n = 157), Terai 0.491 (0.451–0.530, n = 647). Mountain's is widest: smallest group.
  8. Phone sampling misses households without phones (likely poorer → bias up); people under-report income; non-response; mismeasured informal income. The CI covers only random sampling error.
  9. With five values a resample can only rearrange/repeat five numbers; the bootstrap distribution is lumpy and too narrow, so intervals are too short (coverage falls). The sample is too small to stand in for the population.
  10. In our test: n = 10 → 89.5% coverage; n = 100 → 94.5%. Percentile bootstrap intervals are too narrow for small samples.

Lesson 2 Make: low birth weight share in the sample ≈ 0.14 (CI ≈ 0.08–0.21). Difference facility − home mean birth weight ≈ +0.01 kg (CI ≈ −0.15 to +0.18): no clear difference. Lesson 3: 200-sample coverage 94.5%.

Real-data exercises: notes

  • R1 July totals vary a lot year to year; the interval for the mean is much narrower than the range of individual Julys — a perfect illustration of the "not individual values" point. Trends make "the mean of 30 years" a moving target.
  • R2 Gentoo is clearly heavier; Adelie and Chinstrap intervals overlap.
  • R3 NLSS/LFS reports contain standard-error tables in appendices.