In a random sample of 615 people 72 said they would rather e

In a random sample of 615 people, 72% said they would rather eat worms than take a stats test. How confident can you bet that between 70 and 74% of the general population feels this way?

Solution

The probability is
P(0.7<phat<0.74)

=P((0.7-0.72)/sqrt(0.72*(1-0.72)/615) <(phat-p)/sqrt(p*(1-p)/n) <(0.74-0.72)/sqrt(0.72*(1-0.72)/615))

=P(-1.10<Z<1.10) =0.7287 (from standard normal table)

So we have 72.87% confident.