The Wobble Frame

The estimate wobbles. The standardfeil measures the wobble. The confidence interval frames it with an explicit error rate.

The estimate is not the truth. Every sample gives a different x̄. The wobble piles up into a bell (SGS approved). The frame is two walls around where your dart landed, wide enough that the truth is probably inside. Repeat a thousand times — 95% of frames catch μ. 5% miss.

Which frame are you building?

σ kjent — z-KI. Wobble: σ/√n. Stretch factor from z-table.

σ ukjent — t-KI. Wobble: s/√n. Stretch factor from t-table, df = n−1.

Andel (proportion) — z-KI. Wobble: √(p̂(1−p̂)/n). Stretch from z-table.

The Frame

z-Frame

σ known — normal bell. 95% confidence, n = 36.

Eksamen Checklist

1. σ kjent or ukjent? → z-table or t-table

2. Konfidensnivå? → α → α/2 → stretch factor from table

3. n? → √n for wobble, df = n−1 if using t

4. x̄ (or p̂) and the wobble? → center and margin → frame

Connected Spells

Bell-Walk gives the bell. The Bell-Walk (Kap 7) is the foundation — the Wobble Frame builds the frame on top of it.

Weighing Table gives σ and s. The Weighing Table (Kap 5+6) measures the spread that feeds the wobble.

The next spell, T_obs, flips the question: instead of framing the truth, you test a specific claim against the wobble.

Formula Reference — Kap 8

z-KI (σ kjent)Kap 8

x̄ ± z_α/2 · σ/√n

Wobble: σ/√n. Stretch: z-table. The pure normal frame.

t-KI (σ ukjent)Kap 8

x̄ ± t_{α/2, df} · s/√n

Wobble: s/√n. Stretch: t-table, df = n−1. Fatter tails → wider frame.

Proportion KIKap 8

p̂ ± z_α/2 · √(p̂(1−p̂)/n)

Wobble: √(p̂q̂/n). Always z-frame — proportions have built-in variance.

Common z-valuesTable

90%: z = 1.645 95%: z = 1.960 99%: z = 2.576

Higher confidence → more wobbles → wider frame → less precise but more honest.