What am I doing wrong in finding the confidence interval? In a certain bio-engineering experimen

Terrence Riddle

Terrence Riddle

Answered question

2022-04-16

What am I doing wrong in finding the confidence interval?
In a certain bio-engineering experiment, a successful outcome was achieved 60 times out of 125 attempts.
Construct a 95% confidence interval for the probability, p, of success in a single trial.
My answer:
We know that the confidence interval is:
(pks,p+ks)
Where s is the standard error.
I found the k value using Matlab code:
k=v(0.975)=1.9600
Also: p=60125=0.48
Standard Error:
s=p(1p)n=0.480.52125=0.04469
We get the Confidence Interval:
(0.392,0.568)
But my answer is wrong. Is there anything I'm missing out here?

Answer & Explanation

gsmckibbenx7ga

gsmckibbenx7ga

Beginner2022-04-17Added 17 answers

If X=60 successes in n=125 binomial trials, maybe your text is using the confidence interval that 'appends 2 successes and 2 failures' to the data before computing the CI. Such CIs have been shown to have more accurate coverage probabilities than the traditional ones. Then p+=60+2125+4=.4806 and n+=129 so that the CI is (0.394,0.567).
If that is not the 'correct answer' you're looking for, please do tell us what it is.

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