Week 8 · Applied Statistics · HEG Genève

Do lakeside pizzerias really charge more?

One sample tested one claim. Most business questions compare two things: two neighbourhoods, before and after a menu change, two proportions. This week is the two-sample toolkit — independent samples large and small, paired samples, two proportions — and, above all, the judgement of which one applies.

🏫 In class: 3 h · lesson ~1 h, then exercises ~2 h 📖 Saylor ch. 9 ▶ The Lecture button shows the slide outline

By the end of Week 8 you will be able to

Build a confidence interval and a test for the difference of two means with large independent samples.
Do the same with small samples using the pooled t.
Tell paired from independent samples, and run the paired test on the differences.
Compare two proportions.
Choose the right two-sample procedure for a business question — the exam's real test.

Resources

✓Saylor §9.1 — Two means, large independent samples ↗

✓Saylor §9.2 — Two means, small independent samples ↗

✓Saylor §9.3 — Paired samples ↗

✓Saylor §9.4 — Two population proportions ↗

✓Saylor §9.5 — Sample size considerations ↗

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

Exam cards c16–c19

← Course page

Section 8.1 · The hook

Lake vs station

Planned · Hook

Estimate the price gap between lakeside and station pizzerias

Slider: "lakeside pizzerias charge on average __ francs more." Lock it.

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 8.2 · Two means, large samples

The difference and its standard error

Planned · Independent

x̄₁ − x̄₂ and √(σ₁²/n₁ + σ₂²/n₂) (§9.1)

Widget: two strips of prices (lake, station); the difference of means, its standard error, the interval and the z test. Exam card c16.

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 8.3 · Two means, small samples

Pooled t

Planned · Pooled

s_p² and df = n₁ + n₂ − 2 (§9.2)

Widget: the same with 8 and 10 pizzerias; pooled variance built step by step. Exam card c17.

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 8.4 · Paired samples

Before and after the new menu

Planned · Paired

The test on the mean difference d̄ (§9.3)

Widget: the same 12 pizzerias before and after; watch the paired analysis find a difference the independent one misses — variance between pizzerias vanishes.
Classify (6 rows): paired or independent? — the most important six rows of the semester. Exam card c18.

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 8.5 · Two proportions

Share over CHF 20, lake vs station

Planned · Proportions

p̂₁ − p̂₂ and the pooled proportion (§9.4) · sample size (§9.5)

Widget: two proportions, the pooled p̂ for the test, the unpooled SE for the interval. Exam card c19.

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 8.6 · Checkpoint

Prove it to yourself

Planned · Quiz

Self-check quiz & where this goes next

Ten questions: SE of a difference, a two-sample z, a pooled t, paired vs independent ×3, two proportions, and one sample-size question.

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 8.7 · Workshop

The pizzeria file · instalment eight

Planned · Exercise

Workbook fields

w8_design — an A/B test for your pizzeria (two recipes, two prices, two evenings): what is compared, paired or independent, and why.
w8_result — what result would make you change the menu, in numbers.

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 · ~115 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 · Independent or paired? 12 min
eight designs — the decision that carries the chapter
Exercise 2 · The SE of a difference 12 min
√(σ₁²/n₁ + σ₂²/n₂), and why it is not σ₁ + σ₂
Exercise 3 · Two means, large samples 18 min
lake vs station: the interval and the test
Exercise 4 · Pooled variance 15 min
s_p² step by step, df = n₁ + n₂ − 2
Exercise 5 · Two means, small samples 15 min
eight and ten pizzerias, the pooled t
Exercise 6 · The paired test 18 min
the same twelve before and after — and what the independent test misses
Exercise 7 · Two proportions 15 min
pooled p̂ for the test, unpooled SE for the interval
Exercise 8 · Design your A/B test 10 min
two recipes, two evenings: what is compared, and how

Status → outline only. Nothing here is interactive or counted yet.

Course page →