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It’s not a particularly precise estimate because of the small sample size. A rough approximation to the 95 percent confidence interval for a proportion is
![\[ \hat{p}\pm 1.96\sqrt{\hat{p}(1-\hat{p})/n} \]](https://yanzhou.de/wp-content/ql-cache/quicklatex.com-486001bb9e0a267ab52a5e8b044a6fad_l3.png "Rendered by QuickLaTeX.com")
where p̂ is the estimate of the proportion, 0.55 in our case, and n is the sample size. Thus, the probability that the population allele frequency falls within the interval (0.256, 0.844) is 0.95.
Note:
![\[\hat{p}\pm z\sqrt{\hat{p}(1-\hat{p})/n}\]](https://yanzhou.de/wp-content/ql-cache/quicklatex.com-273b606af039c90de7af2d97a0dc40eb_l3.png "Rendered by QuickLaTeX.com")
Where z is 1-α/2 the quantile of a standard normal distribution (i.e., the probit) corresponding to the target error rate α. For a 95% confidence level, the error α=1-0.95=0.05, so 1-α/2=0.975 and z=1.96.
Binomial proportion confidence interval
Python
from statsmodels.stats.proportion import proportion_confint
proportion_confint(count=6,nobs=11, alpha=(1 - 0.95))statsmodels.stats.proportion.proportion_confint
(But when I tried to use method “binom_test”, it caused \”kernel restart” issue in Jupyter Notebook…)