Practice prompt · Q:statistics-estimation-and-uncertainty/precision-boundary-001

Compute Year 1 interval width and preserve its boundary

Reproduce the supplied t margin and endpoints without treating sampling precision as data quality proof.

Updated Aug 7, 2026 Review due Nov 7, 2026

Practice

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Year 1 has x-bar = 31.875 days, s = 5.852349955 days, n = 16, and supplied t* = 2.131449545559323. Which calculation and boundary are correct?

The answer requires both mathematical reconciliation and an explicit limit on what the interval can validate.

Choose the best answer. a MOE = 12.47 days because t* must multiply s directly; the interval proves source accuracy. b MOE = 3.118497163 days and the interval is [28.756502837, 34.993497163]; source and frame error remain separate. c MOE = 0.194906073 days because divide by n twice; all larger uncertainty is nonsampling error. d The endpoints are 28.76 and 34.99, so their midpoint is exactly 31.88 and no reconciliation is needed.

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Answer: b

Choice b. SE = 1.4630874888399532; MOE = 3.1184971632014493; subtract and add that full-precision margin. Frame and measurement review remain independent.