Binomial Confidence Interval

References

• R binom.test help

     Confidence intervals are obtained by a procedure first given in
     Clopper and Pearson (1934).  This guarantees that the confidence
     level is at least ‘conf.level’, but in general does not give the
     shortest-length confidence intervals.

95 percent confidence intereval

res <- sapply(c(28,18,7,6,3,3, 36,30,15,14,4,3),
              function(x) {

                  res <- binom.test(x = x, n = 55)
                  c(res$statistic, res$estimate, res$conf.int)
              })

t(round(res, 3))

##       number of successes probability of success            
##  [1,]                  28                  0.509 0.371 0.646
##  [2,]                  18                  0.327 0.207 0.467
##  [3,]                   7                  0.127 0.053 0.245
##  [4,]                   6                  0.109 0.041 0.222
##  [5,]                   3                  0.055 0.011 0.151
##  [6,]                   3                  0.055 0.011 0.151
##  [7,]                  36                  0.655 0.514 0.778
##  [8,]                  30                  0.545 0.406 0.680
##  [9,]                  15                  0.273 0.161 0.410
## [10,]                  14                  0.255 0.147 0.390
## [11,]                   4                  0.073 0.020 0.176
## [12,]                   3                  0.055 0.011 0.151