There are various styles of confidence intervals (CIs). The 95% Wald CI discussed in @Jeff's Answer (+1) sometimes have 95% coverage of the true population proportion for large $n.$ But for small $n$ the estimated standard error $\sqrt{\frac{\hat p(1-\hat p)}{n}}$ may not be sufficiently close to the true standard error
$\sqrt{\frac{p(1-p)}{n}}$ to give good results. [Also for observed
proportions near $0$ or $1,$ endpoints of Wald intervals may extend outside
of the interval $(0,1)$ or the intervals may be of length $0.]$
You can read Wikipedia on binomial confidence intervals to see a discussion of various styles of CIs,
some of which give good results for small $n.$
The Jeffreys interval estimate is based on a Bayesian argument starting with a non-information Jeffreys prior $\mathsf{Beta}(.5. .5).$ It also has good
frequentist properties, covering the true proportion $p$ with nearly the 'promised' long-run frequency--for small and large sample sizes $n.$
For your situation with an observed proportion of 937 out of 1008, a 95% Jeffreys CI consists of quantiles 0.025 and 0.975 of
$\mathsf{Beta}(.5+937, .5+1008-937)$ $\equiv
\mathsf{Beta}(937.5, 71.5),$ which is easily computed in R as $(0.913,0.944).$
qbeta(c(.025,.975), 937.5, 71.5)
[1] 0.9125267 0.9441387
Perhaps no style of confidence interval may be ideal for all purposes,
but it is worthwhile knowing the advantages and disadvantages of
several styles CIs.
Ref: For graphs of coverage probabilities of Jeffreys CIs.
