Question 1157866
The half-interval for CI=95% is z(1.96)*sqrt(p(1-p)/n)
that is added and subtracted to the point estimate of 35%
SE=sqrt(.35*.65/450)=0.0005056=0.0225
1.96*0.0225=0.0440
95% confidence interval for the true proportion is (0.306, 0.394) This means that we don't know the exact proportion of people who are hoping. That is a parameter and will never be known, but we can be highly confident that the interval will contain that value.
Note: this will be different on a calculator, because 35% of 450 is not an integer, so one has to use 157/450 or 158/450, giving a slightly different interval from 157.5/450