You have a sample mean of .53 or 725.57 people. This is a binomial distribution, so the variance is np(1-p) or 341.02 people which leads to a standard deviation of 18.47 people.
A 95% confidence interval leads to a range to about two standard deviations away from the mean. The exact amount is 1.96 SD's away, so the range of values to be 95% confident that the population mean is within that range is:
Our null hypothesis claims a mean of 684.5 (50% of 1369). That hypothesized mean is not within our range, so we must fail to accept the null hypothesis (aka accept the alternate).
BTW. 1369 is 37 squared, and 13 squared is 169