Calculate a 95% confidence interval

Suppose we conduct a survey in a city in order to estimate the proportion of individuals in favor of funding the Sports and Entertainment corporation. We sample n = 15 city blocks and interview everyone in the blocks
chosen. Define mi to be the number of residents and ai to be the number
favoring support in block i. The estimate of the population proportion is seen
to be
pˆ =
= 0.709
Using that estimate, we compute from the data the differences yi − ym¯ i
and construct the table below
n sum mean standard deviation
mi 15 911 60.73 14.007
ai 15 646 43.07 9.5728
ai − pmˆ i 15 0 0 6.2230
Calculate a 95% confidence interval for the population proportion