confidence_interval

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Compute a confidence interval for a mean (normal approximation). FREE. Typical input {"mean": 72.4, "std_dev": 8.1, "n": 64, "confidence_pct": 95} returns {"mean": 72.4, "margin_of_error": 1.9845, "interval": [70.4155, 74.3845], "note": "..."}. Use on data already collected, for a mean. Normal approximation, so it is unreliable on very small or heavily skewed samples. Not for proportions or two-group comparisons - the data server's ab_test compares two proportions. Errors: on invalid, missing, or malformed input this tool never raises a protocol error — it returns {"error": "<what is wrong and how to fix it>"} (for example {"error": "confidence 90/95/99, n>=2, std_dev>=0"}). Every call is read-only and idempotent, so after correcting the input it is always safe to retry.