First, confidence intervals for number of murders, printed below. All include 16.

library(PropCIs)
#assuming Manhattan population of 1630000 (close enough)
ans=add4ci(x=11,n=1630000,conf.level=0.95)
ans$conf.int[1:2]*1630000
## [1]  5.933263 20.066673
ans=addz2ci(x=11,n=1630000,conf.level=0.95)
ans$conf.int[1:2]*1630000
## [1]  5.875571 19.965827
ans=exactci(x=11,n=1630000,conf.level=0.95)
ans$conf.int[1:2]*1630000
## [1]  5.491176 19.681934

Direct comparison of 11 to 16. Confidence interval of difference, according to every test, includes 0 (printed below), meaning no significant difference.

ans=wald2ci(11,1630000,16,1630000,.95,adjust="AC")
ans$conf.int[1:2]*1630000 #includes zero, meaning no significant difference
## [1] -15.554662   5.554674
ans=wald2ci(11,1630000,16,1630000,.95,adjust="Wald")
ans$conf.int[1:2]*1630000 #includes zero, meaning no significant difference
## [1] -15.184228   5.184228
ans=diffscoreci(11,1630000,16,1630000,.95)
ans$conf.int[1:2]*1630000 #includes zero, meaning no significant difference
## [1] -16.17286   5.58999

Direct comparison of 31 to 50 shooting incidents. Confidence interval of difference, according to every test, narrowly excludes 0 (printed below), meaning a (marginal) significant difference!

ans=wald2ci(31,1630000,50,1630000,.95,adjust="AC")
ans$conf.int[1:2]*1630000 #includes zero, meaning no significant difference
## [1] -36.855837  -1.144116
ans=wald2ci(31,1630000,50,1630000,.95,adjust="Wald")
ans$conf.int[1:2]*1630000 #includes zero, meaning no significant difference
## [1] -36.639445  -1.360555
ans=diffscoreci(31,1630000,50,1630000,.95)
ans$conf.int[1:2]*1630000 #includes zero, meaning no significant difference
## [1] -37.556498  -1.414637