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

Annotations already establish the safety profile (readOnlyHint, idempotentHint, openWorldHint=false), so the bar is lower. The description adds genuine value by disclosing what the tool returns (margin of error, critical value, every step shown), which matters because no output schema exists.

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

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

A single information-dense sentence leads with the core capability, and the trailing documentation URL is clearly segregated. Nothing is redundant, though the URL consumes space without aiding tool selection.

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

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

For a six-parameter, zero-required, no-output-schema tool with full schema coverage, the description is nearly sufficient: it tells the agent what inputs map to which methods and what outputs to expect. Minor gaps remain on how x/n interact for the proportion mode and how SD is handled for the z variant.

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

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

Schema description coverage is 100% and all six parameters are individually documented with ranges, defaults and enums, so the schema carries the parameter burden. The description's mention of t/z, Wald/Wilson and 80–99.9% only echoes the type and conf enums rather than adding new semantics.

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

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

The description names a specific statistical resource (confidence intervals for a mean via t/z, or a proportion via Wald/Wilson) and even enumerates the supported confidence levels and computed outputs. That specificity naturally separates it from adjacent siblings like p_value_calculator or standard_deviation_calculator, though no sibling is named explicitly.

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

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

Usage is implied by the stated scope: use it when you need an interval for a mean or a proportion. However, there is no explicit guidance on when to prefer mean-t vs mean-z vs prop, nor any exclusion pointing to alternative tools for related statistical needs.

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