# problem-8.6

problem-8.6 The key to solving this is to find the value of z so that P(\phat > z) = 0.05. This is answered using the quantiles of the normal distribution, as \phat is approximately normally distributed with mean p=0.113 and standard deviation Ö{p(1-p)/n}.

    > p = .113; n = 50000; qnorm(.95, mean=p,sd=sqrt(p*(1-p)/n))
    [1] 0.1153

Multiplying by n produces the cutoffs

    > n*0.1153
    [1] 5765

Any value of 5,765 or larger would give a p-value less than 0.05.