Question

Derive 100(1−α) percent lower and upper confidence intervals for p, when the data consist of the values of n independent Bernoulli random variables wi

Upper level probability
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asked 2021-05-29

Derive \(100(1-\alpha)\) percent lower and upper confidence intervals for p, when the data consist of the values of n independent Bernoulli random variables with parameter p.

Expert Answers (1)

2021-05-30
Lower confidence interval: \(\displaystyle{\left(-\infty,\overbrace{{{p}}}+{z}_{{\alpha}}\sqrt{{\overbrace{{{p}}}{\left({\frac{{{1}-\overbrace{{{p}}}}}{{{n}}}}\right)}}}\right.}\)
Upper confidence interval: \(\displaystyle{\left(\overbrace{{{p}}}-{z}_{{\alpha}}\sqrt{{\overbrace{{{p}}}{\left({\frac{{{1}-\overbrace{{{p}}}}}{{{n}}}}\right)},\infty}}\right\rbrace}\)
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