Answer: 0.4521 - 0.4879
Step-by-step explanation:
1) Find the standard deviation with the given information:
n=3000
p=47% ⇒ 0.47
1-p= 1 - 0.47 = 0.53
[tex]\sigma =\sqrt{\dfrac{p(1-p)}{n}}\\\\\\.\ =\sqrt{\dfrac{0.47(0.53)}{3000}}\\\\\\.\ =\sqrt{\dfrac{0.2491}{3000}}\\\\\\.\ =\sqrt{0.00008303}\\\\\\.\ =0.009112[/tex]
2) Find the margin of error (ME) with the given information:
C=95% ⇒ Z = 1.960
σ=0.009112
ME = Z × σ
= 1.96 (0.009112)
= 0.01786
3) Find the confidence interval with the given information:
p = 0.47
ME = 0.01786
CI = p ± ME
= 0.47 ± 0.01786
= (0.4521, 0.4879)
