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.
We know that the confidence interval is:
$$(p-ks,p+ks)$$ Where s is the standard error.
I found the k value using Matlab code:
We get the Confidence Interval:
But my answer is wrong. Is there anything I'm missing out here?
In the next part:
The researchers expected a successful outcome 70% of the time. Is the data consistent with this hypothesis?
Obviously, 0.7 doesn't lie in the Confidence Interval which I calculated (which is wrong). So, how do we approach such a problem?