Question

7) A researcher conducts a poll to study the level of educational attainment in a certain state.

Of the 214 people surveyed by the researchers, 34 had a bachelor's Degree.

a) Find a 90% confidence interval for the true proportion of people the state with bachelor's degrees.

b) Provide the right endpoint of the interval as your answer.

Round your answer to 4 decimal places.

Answer 1

sample proportion, = 0.1589
sample size, n = 214
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.1589 * (1 - 0.1589)/214) = 0.025

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, Zc = Z(α/2) = 1.64

Margin of Error, ME = zc * SE
ME = 1.64 * 0.025
ME = 0.041

CI = (0.1589 - 1.64 * 0.025 , 0.1589 + 1.64 * 0.025)
CI = (0.1179 , 0.1999)

b)

Right endpoint = 0.1999