Manuscript Oai265-B@2 · Oai265-B-v2.tex · corollary · 94b6f42f

Corollary: Informative all-pass sample threshold

Supplied script execution report and its interpretation › Why zero invalid acceptances is non-informative here · lines 1411–1433 · proof included or linked

Oai265-B@2#cor:2871

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For the same risk and allowances, exact binomial endpoints accept all-pass data at $ε = 0.1$ precisely when

n \geq ⌈ \frac{lo g 120}{- lo g ( 599/600 )} ⌉ = 2871

shots per setting.

Proof. Use (eq:cpSamples) with $q = 1/400$ . The integer boundary can be checked without logarithm rounding by

12059 9^{2870} > 60 0^{2870}, 12059 9^{2871} < 60 0^{2871} .

Displayed formulas in this passage

unlabeled · line 1415
$n \geq ⌈ \frac{lo g 120}{- lo g ( 599/600 )} ⌉ = 2871$
unlabeled · line 1428
$12059 9^{2870} > 60 0^{2870}, 12059 9^{2871} < 60 0^{2871} .$

Nearby in this section

proposition: Proposition: No 0.1 acceptance at the reported sample count
section: Why zero invalid acceptances is non-informative here
section: Why zero invalid acceptances is non-informative here