Confidence Intervals for a Bernoulli θ

Abstract

Let X be the total number of “successes” in a random sample of n Bernoulli trials with P(S) = θ= 1 — P(F); the distribution of X is binomial. (Usually “p” is used for this parameter; the Greek analogue π has another meaning so we useθ.) We could rewrite lessons 15 and 16 to develop a test for

H_o: θ = θ_oversus H_a: θ = θ_a>θ_o.

Instead,We Consider a “two-sided hypothesis”

H_o: θ = θ_oH_a:θ≠θ₀.