For a 95% confidence interval we use the formula
p ± z*√(p(1-p) / n)
The sample size is 500, so n = 500.
First, we need to establish the sample proportion, which is the number of people in the sample who liked the candidate to the total sample size.
p = (#people who liked candidate) / (sample size n)
p = 315 / 500 = 0.63
The critical value z* for 95% confidence interval is 1.960.
Summarize:
n = 500
z* = 1.960
p = 0.63
(1-p) = 1-0.63 = 0.37
so we are ready to plug into original formula!
p ± z*√(p(1-p) / n)
=0.63 ± 1.960 √((0.63 × 0.37) / 500)
=0.63 ± 1.960 √(0.2331 / 500)
=0.63 ± 1.960 √(0.0004662)
=0.63 ± (1.960 × 0.021591665)
=0.63 ± (0.042319664)
round to 2 sig figs
=0.63 ± 0.042
which gives the upper confidence limit of
0.63 + 0.042
= 0.672 or 67.2 %
and a lower confidence limit of
0.63 - 0.042
= 0.588 or 58.8%
ANSWER:
0.588 < p < 0.672
OR
58.8% < p < 67.2%
Good luck! Hope this helps :)
