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tresor4k

macalc

calculate_confidence_interval

Compute confidence intervals for sample means. Input mean, standard deviation, sample size, and confidence level (90%, 95%, or 99%) to get lower and upper bounds. Ideal for statistics, A/B tests, and 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.
Behavior2/5

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

No annotations are provided, so the description must carry the full burden. It fails to disclose important assumptions (e.g., normal distribution, t- vs z-test), edge cases (small samples), or formula used; only mentions inputs and output bounds.

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

Conciseness4/5

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

The description is two main sentences plus a pointer to list_bundles. It is concise and front-loaded with the purpose, though the pointer is somewhat extraneous but not harmful.

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

Completeness2/5

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

Given the tool's statistical nature and the presence of an output schema, the description still lacks key contextual information such as distribution assumptions and prerequisites. It is incomplete for a tool among many similar calculators.

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%, so baseline is 3. The description lists the same inputs as the schema without adding new semantic details like units or typical ranges, offering no added value beyond the schema.

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

Purpose4/5

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

The description clearly states 'Compute confidence interval for a sample mean' with specific use cases (statistics, A/B testing, polling). It distinguishes from siblings via the name and use case hints, though not explicitly.

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 provides context for use ('statistics, A/B test results, or polling') and points to list_bundles for related calculators, but does not specify when not to use this tool or compare to alternatives like calculate_sample_size.

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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