the proportion of industries that are heavy polluters, call it

Your null hypothesis is that , under this hypothesis the expected number of heavy polluters in a sample of is .what hypothesis test do i need to do??

The sample size is not your problem you are given a sample of size , also you appear to be confusing hypothesis testing with construction of a confidence interval. With a confidence interval we construct an interval from the experimental results that will contain the true value the proscribed proportion of the time, with a hypothesis test we assume the null hypothesis and compute the probability that we would get a result at least as extreme as that observed by chance given that the null hypothesis is true, and accept or reject the null hypothesis on the basis of this probability.and if i have a 95% confidance interval, (standard error of 0.05), what sample size do I need

RonL