Question

You are interested in constructing a 95% confidence interval for the proportion of Americans who believe that evolution of species is false. Of the 1200 randomly selected Americans surveyed, 671 believe that evolution of species is false.

Answer 1

Solution

Let p = proportion of Americans who believe that evolution of species is false.

Back-up Theory

100(1 - α)% Confidence Interval for binomial p = pcap ± Z_α/2SE(pcap)

= pcap ± Z_α/2√{pcap(1 - pcap)/n}, where pcap = sample proportion, Z_α/2 = upper (α/2) percent point of N(0, 1) and n = sample size.

Now to work out the solution,

Given, ‘Of the 1200 randomly selected Americans surveyed, 671 believe that evolution of species is false.’ => pcap = 671/1200 =

And 95% CI => α = 0.05 and so Z_α/2 = upper 2.5% point of N(0, 1) = 1.96 [from Standard Normal Tables.]

	pcap =	0.55917	1-pcap =	0.44083
99% CI for p:		0.55917	±	0.02809
Lower Bound =		0.53108
Upper Bound =		0.58726