HEG Genève APPLIED STATISTICS · WEEK 7 ← Course
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🔧 Week 7 is in preparation. What follows is the plan for the 3-hour session — objectives, the Part 1 sections, the Part 2 exercise outline and the slide outline. Nothing here is counted yet.
Week 7 · Applied Statistics · HEG Genève

A competitor claims the Geneva average is CHF 20. Is it?

Estimation says where the truth probably is; testing asks whether a specific claim survives the data. This week is the logic of hypothesis testing — null and alternative, test statistic, rejection region, the two kinds of error — then the one-sample z test, the p-value, the small-sample t test, and the test for a proportion.

🏫 In class: 3 h · lesson ~1 h, then exercises ~2 h 📖 Saylor ch. 8 ▶ The Lecture button shows the slide outline

By the end of Week 7 you will be able to

  • Write H₀ and Hₐ for a claim, and choose left-, right- or two-tailed.
  • Run a large-sample z test for a mean with a rejection region at level α.
  • Compute and interpret a p-value — and say what it is not.
  • Run a small-sample t test and a test for a proportion.
  • Name Type I and Type II errors in the pizzeria's terms, and say which α trades against which.

Resources

✓Saylor §8.1 — The elements of hypothesis testing ↗
✓Saylor §8.2 — Large-sample tests for a population mean ↗
✓Saylor §8.3 — The observed significance of a test ↗
✓Saylor §8.4 — Small-sample tests for a population mean ↗
✓Saylor §8.5 — Large-sample tests for a population proportion ↗
Homework for this week is written with the week itself, on the Week 1–2 pattern: a fresh dataset, hints and worked solutions.
Tools for this week
Real or random? — signal vs noise, againExam cards c13–c15
← Course page
Section 7.1 · The hook

The CHF 20 claim

Planned · Hook

Estimate: is CHF 19.6 from 30 pizzerias "different enough" from 20?

  • Slider: "how sure are you the true average is NOT 20?" Lock it; section 7.4 gives the p-value.
Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.
Section 7.2 · The logic

Innocent until the data say otherwise

Planned · Logic

H₀, Hₐ, test statistic, rejection region, Type I and II errors (§8.1)

  • Classify (6 rows): write the hypotheses — left, right or two-tailed — for six pizzeria claims.
  • Widget: the two errors as a 2×2 — "we change the price when we shouldn't" vs "we keep it when we should change" — with α and β on sliders.
Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.
Section 7.3 · The z test

Large samples

Planned · z test

Rejection region at α = 0.05, 0.01 (§8.2)

  • Widget: the standard normal with the rejection region shaded for the chosen tail and α; type x̄, n, σ and watch the test statistic land inside or outside. Exam card c13.
Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.
Section 7.4 · The p-value

How surprising is this?

Planned · p-value

Observed significance (§8.3)

  • Widget: the p-value as the tail area beyond the observed statistic; compare with α. The hook closes: p-value for x̄ = 19.6, n = 30, σ = 4 against µ₀ = 20.
  • The five-line list of what a p-value is NOT — the exam's favourite trap.
Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.
Section 7.5 · t and proportions

Small samples, and shares

Planned · t & p

Small-sample t test (§8.4) · test for a proportion (§8.5)

  • Widget: the t test with df = n − 1 on a sample of 12 lakeside pizzerias; the proportion test on "more than 30% charge over CHF 20". Exam cards c14–c15.
Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.
Section 7.6 · Checkpoint

Prove it to yourself

Planned · Quiz

Self-check quiz & where this goes next

  • Ten questions: hypotheses, tails, the rejection region, a z statistic, a p-value interpretation, Type I vs II, a t test, a proportion test, and "significant ≠ important".
Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.
Section 7.7 · Workshop

The pizzeria file · instalment seven

Planned · Exercise

Workbook fields

  • w7_claim — a claim about your pizzeria you would test, with H₀ and Hₐ.
  • w7_errors — the Type I and Type II error for that test, in plain words, and which one costs you more.
Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.
Course page →
Part 2 · Exercises

8 exercises, worked together

Planned · ~103 min

The second half of the session

When this week is written, each exercise below becomes a form on this page and a slide in the deck, generated from one array so the two can never disagree — and its solution opens when the instructor reveals it in class. Same engine as Weeks 1–2 (exercises.js).

  • Exercise 1 · Write the hypotheses  12 min
    six claims → H₀, Hₐ, and the tail
  • Exercise 2 · The rejection region  15 min
    a z test at α = 0.05 on the CHF 20 claim
  • Exercise 3 · Change α  10 min
    0.10, 0.05, 0.01 — what moves, and what it costs
  • Exercise 4 · Compute a p-value  15 min
    the same test, the other way round
  • Exercise 5 · What a p-value is not  12 min
    five statements — spot the three that are wrong
  • Exercise 6 · Type I or Type II?  12 min
    name both errors for the pizzeria, and price them
  • Exercise 7 · A small-sample t test  15 min
    twelve lakeside pizzerias, df = 11
  • Exercise 8 · A test for a proportion  12 min
    “more than 30% charge over CHF 20”
Status → outline only. Nothing here is interactive or counted yet.
Course page →