Is it true that Wilson score interval with continuity correction is strictly conservative? I mean, is its actual coverage probability always not less than its nominal confidence coefficient?

UPDATE: no, see Newcombe (1998) http://www.stats.org.uk/statistical-inference/Newcombe1998.pdf

If not, are there confidence intervals for binomial proportion which are 1) strictly conservative, 2) easily computable by explicit formulas, 3) of practical value?

For the Agresti-Coull interval, it is known that its actual (minimum) coverage probability depends on n and is less than its nominal confidence coefficient. Is it known whether the actual coverage probability approaches the nominal confidence coefficient as n goes to infinity?

mayeventually answer but the chance is not terribly high. Remember that you ask a mixed audience, not just one specialist in your particular field when posting on MO and other math. sites :) – fedja May 26 '11 at 13:40