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Galdr Spell · Kap 9 + 10

Tobs — Distance in Wobbles

The gap between a claim and a handful, measured in the bell's own ruler. One number tells you: forkast or behold.

Distance only means something when you state the unit. 12 000 kroner is meaningless. It could be enormous or trivial. 12 000 kroner in a field where the typical wobble is 6 000 is two wobbles. Two wobbles is a coordinate you can read on the bell.
Which test are you running?
σ kjent — z-test. Wobble: σ/√n. Critical value from z-table.
σ ukjent — t-test. Wobble: s/√n. Critical value from t-table, df = n−1.
μ ≠ μ&sub0; — tosidig (two-tailed). Rejection in both tails, α/2 each.
μ > μ&sub0; or μ < μ&sub0; — ensidig (one-tailed). All α in one tail.
Choose the test
The Bell

Tosidig t-test

df = 24, α = 0.05. Rejection in both tails.

Walk the spell
Eksamen Procedure
1. Set up H\u2080 and H\u2090. What is the claim? What is the alternative?
2. σ kjent or ukjent? → z-test or t-test
3. Tosidig or ensidig? → determines where the rejection zone sits
4. Find critical value from table (α, df)
5. Calculate Tobs = (x̄ − μ\u2080) / (s/√n)
6. Compare. Past the wall → forkast. Inside → behold.
Connected Spells

Wobble Frame builds the frame. Tobs flips the question: instead of framing the truth, you test a specific claim. The Wobble Frame (Kap 8) is the mirror image.

Bell-Walk gives the bell. The Bell-Walk (Kap 7) is the foundation the test lives on.

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

Formula Reference — Kap 9 + 10
Tobs (σ ukjent)Kap 9
Tobs = (x̄ − μ0) / (s/√n)
The gap in wobbles. s/√n is the ruler. Compare to t-critical with df = n−1.
zobs (σ kjent)Kap 9
zobs = (x̄ − μ0) / (σ/√n)
Same structure, but σ is known. Compare to z-critical.
Decision RuleKap 9–10
|Tobs| > tcrit → Forkast H0   |   |Tobs| ≤ tcrit → Behold H0
Forkast = reject the claim. Behold = keep believing until stronger evidence arrives. Behold ≠ accept.
The Three RunesKeep separate
σ (truth)  ≠  s (estimate)  ≠  s/√n (wobble of x̄)
σ is the real spread. s estimates it. s/√n is how much x̄ wobbles. Tobs counts wobbles, not sigmas.