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tresor4k

macalc

calculate_confidence_interval

Compute confidence interval for a sample mean. Input mean, standard deviation, sample size, and confidence level to get lower and upper bounds for statistics, A/B tests, or polling.

Instructions

Compute confidence interval for a sample mean. Use for statistics, A/B test results, or polling. Inputs: mean, std dev, sample size, confidence (90/95/99%). Returns CI lower/upper bounds. See list_bundles for related 'math' calculators.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
sample_meanYesSample mean
std_devYesStandard deviation
sample_sizeYesSample size
confidenceNoConfidence level95

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
resultNoComputed result. Object whose fields depend on the tool (e.g. {tax, marginal_rate, brackets} for tax tools, {volume_l, gallons} for volume tools).
formulaNoHuman-readable formula or method used (e.g. "I=P·r·t", "Magnus formula").
sourceNoAuthoritative source for the rule or formula (e.g. "Article 197 CGI", "NF DTU 21").
reference_urlNoLink to a calcul2 page documenting the calculation in detail.
Behavior4/5

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

No annotations exist, so the description carries full burden. It explicitly states the tool returns CI lower/upper bounds, which is the primary behavior. For a pure calculator, this is sufficient and transparent.

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?

The description is extremely concise (two sentences), front-loads the purpose, and efficiently covers usage, inputs, outputs, and a cross-reference. No wasted words.

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

Completeness4/5

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

Given an output schema exists, the description adequately explains returns. It covers purpose, parameters, and usage context. The reference to list_bundles adds completeness.

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

Parameters3/5

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

Schema coverage is 100%, and the description lists the inputs (mean, std dev, sample size, confidence) with examples. However, it adds limited new semantic value beyond the schema descriptions.

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?

The description clearly states the tool computes a confidence interval for a sample mean, using specific verbs and resource. It distinguishes from sibling calculators by highlighting its application in statistics, A/B tests, and polling.

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

Usage Guidelines3/5

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

The description suggests use cases (statistics, A/B tests, polling) and points to list_bundles for related calculators. However, it lacks explicit when-not-to-use guidance or alternatives for non-sample-mean applications.

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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