Using the Agresti-Coull method, what is the 95% confidence interval for the proportion when there are 15 observed successes and 25 observed failures?

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Quizplus · Accepted Answer

The Agresti-Coull method for calculating a 95% confidence interval for a proportion involves adding 2 successes and 2 failures to the observed counts before calculating the interval. This gives us 17 successes and 27 failures. The sample proportion (p̂) is then 17/(17+27) = 0.386. The standard error (SE) is calculated using the formula SE = sqrt(p̂(1-p̂)/(n+4)), where n is the total number of trials (n=44 in this case). Plugging in the numbers, we get SE = sqrt(0.386(1-0.386)/44) ≈ 0.073. The 95% confidence interval is then p̂ ± 1.96*SE, which gives us 0.386 ± 1.96*0.073, or approximately 0.243 to 0.529.

Using the Agresti-Coull Method, What Is the 95% Confidence Interval