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stats.bootstrap_ci

Read-onlyIdempotent

Computes percentile bootstrap confidence intervals for a sample mean or median, returning reproducible interval estimates from decimal string inputs.

Instructions

표본 평균 또는 중앙값의 부트스트랩 신뢰구간을 백분위수법으로 구한다. values는 Decimal 문자열 2개 이상, statistic은 mean 또는 median, confidence는 0과 1 사이 실수(기본 0.95), n_resamples는 100 이상 100,000 이하(기본 1000), seed 기본 42로 같은 입력이면 결과가 재현된다. float64 계산 결과를 유효숫자 10자리 문자열로 돌려준다. 표본이 매우 작으면 구간이 불안정하다.

Input Schema

NameRequiredDescriptionDefault
seedNo
valuesYes
statisticNomean
confidenceNo
n_resamplesNo

Output Schema

NameRequiredDescriptionDefault
nYes
seedYes
_metaNo서버가 붙이는 영수증(integrity), 엔진, 힌트
traceYes계산 근거(tool, formula, inputs, steps, output)
ci_lowerYes
ci_upperYes
statisticYes
confidenceYes
n_resamplesYes
point_estimateYes

Schema Changelog

Changes observed during successful MCP inspections.

  1. First observedv0.3.0

TDQS

A4.6/5.0
Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Goes beyond the readOnly/idempotent annotations by disclosing the reproducibility contract (fixed seed 42, same input yields same output), the return representation (float64 values serialized to 10 significant digits), and the small-sample instability caveat. Nothing contradicts the annotations, though permission/error behavior is unmentioned.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Front-loads what is computed, then parameter rules one after another, then output format and the caveat — no filler. Each clause adds a concrete constraint or behavioral fact.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness5/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a 5-parameter statistical tool with zero schema documentation, the description supplies every constraint an agent needs to form a valid call plus the output precision, and the existing output schema covers the return structure.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters5/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, so the description carries the full burden and does: it documents values (Decimal strings, minimum 2), statistic (mean or median), confidence (0-1 open interval, default 0.95), n_resamples (100–100,000, default 1000), and seed (default 42 for reproducibility). These ranges and allowed values exist only in the description.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

States a precise verb+resource: computing a bootstrap confidence interval for the sample mean or median using the percentile method. An agent can distinguish it from the parametric sibling stats.ci_mean by the explicit "bootstrap" and "percentile method" wording.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

Implies usage through hard constraints (values must contain 2+ Decimal strings, n_resamples >= 100) and warns that very small samples produce unstable intervals. It does not explicitly route the agent between this and stats.ci_mean or say when a non-bootstrap CI is preferable.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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