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

Annotations already declare readOnly, idempotent, non-destructive, so the safety profile is covered. The description adds genuine behavioral context beyond that: the statistical method used per mode (t-based vs Wilson) and the default confidence of 0.95, which an agent cannot infer from the schema since no defaults are declared there.

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?

Two dense sentences with no filler, and the primary capability plus the kind selector are front-loaded. The heavy parenthetical nesting makes it slightly harder to parse than a fully linear phrasing would be, but nothing is redundant.

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?

No output schema exists, so the description should ideally state the return shape (lower/upper bounds, point estimate) and behavior on invalid or underspecified input. For a 7-parameter, zero-required-parameter calculator it is adequate but leaves the agent guessing about output and validation.

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?

With 7 parameters and 0% schema description coverage, the description carries the full burden and does map all of them to modes: data or n/mean/sd for means, successes/n for proportions, kind as selector, confidence with its default. It does not clarify what n means in proportion mode or that sd pairs only with mean, leaving minor ambiguity.

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?

States a specific verb and resource ('Confidence interval for a mean ... or a proportion'), and names the exact statistical methods (t-based, Wilson) plus the two input modes. It is clearly distinguishable from calculation siblings, though it never explicitly contrasts itself with hypothesis_test or distribution.

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?

Implied routing is present: kind = mean vs proportion plus the data-or-summary input forms tell the agent which parameters pair with which mode. There is no explicit when-to-use guidance, no exclusion against the sibling inference tools, and no statement of prerequisites or invalid combinations.

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