The Mechanism · Gated-generation receipt

gen-define-a-confidence-interval-and-give-one-short-worked-examp-1586

stable pending witness
2026-05-29 05:24:33 UTC · anthropic/claude-sonnet-4-5

Prompt

Define a confidence interval and give one short worked example.
63 chars

Generation

# Confidence Interval Definition A **confidence interval** is a range of values that likely contains an unknown population parameter, calculated from sample data. It consists of: - An interval estimate (lower bound, upper bound) - A confidence level (e.g., 95%) indicating how confident we are that the interval captures the true parameter ## Worked Example **Problem:** A sample of 25 students has a mean test score of 78 with a standard deviation of 10. Find a 95% confidence interval for the true mean score. **Solution:** Using the formula: CI = x̄ ± t* × (s/√n) Where: - x̄ = 78 (sample mean) - s = 10 (standard deviation) - n = 25 (sample size) - t* = 2.064 (t-value for 95% confidence, df = 24) Calculation: - Standard error = 10/√25 = 2 - Margin of error = 2.064 × 2 = 4.128 - CI = 78 ± 4.128 = **(73.87, 82.13)** **Interpretation:** We are 95% confident that the true mean test score for all students is between 73.87 and 82.13.
18 tokens in · 308 tokens out · 5911 ms · $0.0047

The four gates

RED
pass
no disqualifying input patterns detected
FLOOR
pass
output above protective minimum; no mismatches
WAY
pass
no declared way_path (Way check NA); no coercion language
EXECUTION
deferred
no witnesses available (Witness Roll not yet constituted)

Verifier results

scripture_anchors NOT_APPLICABLE
0 Scripture citation(s) extracted
theology_doctrine NOT_APPLICABLE
no doctrine keyword patterns detected

Metrics

Total latency
5918.5 ms
Base LLM
5910.8 ms
Verifiers
0.4 ms
Gates
0.1 ms
Cost
$0.0047

Trail

05:24:33 received prompt_chars=63 verifiers=['scripture_anchors', 'theology_doctrine']
05:24:33 red_gate decision=pass reason=no disqualifying input patterns detected
05:24:39 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=18 tokens_out=308 latency_ms=5910.8 cost_usd=0.0047
05:24:39 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:24:39 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:24:39 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:24:39 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:24:39 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:24:39 signed hash_algo=sha256 hash=sha256:191ab0349771aaf67a54ffce4acea2755f9046c7b1eca53f9032baf77bebb6d6

Content hash

sha256:191ab0349771aaf67a54ffce4acea2755f9046c7b1eca53f9032baf77bebb6d6

SHA256 over the canonical JSON (excluding this field). Tamper detection. Ed25519 signing planned for v2 once the operator’s signing key is provisioned on disk.

Bring another teaching · Run a discernment