Let’s assume that a hospital’s neurosurgical team performed 30 procedures for in-brain bleeding last year. Five of these procedures resulted in death within 30 days. If the national proportion for death in these cases is .05, then is there evidence to suggest that your hospital’s proportion of deaths is more extreme than the national proportion? Model both as a binomial and a Poisson, and provide your R code solutions.
\(N=30\) procedures
\(\pi=.05\) (under the null assumption)
\(x=5\)
\(P(X \ge 5 | N = 30, \pi=.05)\)
sum(dbinom(5:30, 30,.05))## [1] 0.01563551The rate is 1.5 per year
\(P(Y \ge 5 | \lambda=1.5)\)
sum(dpois(5:10000,1.5))## [1] 0.01857594