Hi Amy,
Formula for a single-proportion confidence interval is:
CI=p^ +/- z*[sqrt(p^q^/n)]
p^=estimated sample proportion
z*=z critical value
q^=1-p^
n=sample size
To use this formula, we require at least ten "successes" and at least ten "failures," which we can define however we like. In this case, we define success as an adult with children, and it is clear from the numbers that we have more than ten successes and failures, so we proceed with the formula.
p^=160/280=0.571
z*=1.96 (Worth memorizing for 95% confidence level)
q^=1-0.571=0.429
n=280
CI=p^ +/- z*[sqrt(p^q^/n)]
CI=0.571 +/- 1.96[sqrt(0.571*0.429/280)]
CI=0.571 +/- 0.058
CI=(0.513, 0.629)
I hope this helps.
