Home › AP Statistics › Statistics › Confidence Intervals › A telephone poll of 1,000 adult Americans finds …
A telephone poll of 1,000 adult Americans finds that 20% consider crime the main problem facing the country. For a 95% confidence level, z(0.025)=1.96. What is the resulting confidence interval, rounded to two decimals?
A(0.10, 0.30)
B(0.18, 0.22)
C(0.20, 0.22)
D(0.02, 0.20)
Answer & Solution
Correct answer: B. (0.18, 0.22)
1. p' = 0.20, q' = 0.80, and n = 1,000.
2. EBP = 1.96*sqrt((0.20)(0.80)/1000) ≈ 1.96*0.01265 ≈ 0.02.
3. Lower bound: 0.20 - 0.02 = 0.18, and upper bound: 0.20 + 0.02 = 0.22.
4. Option C only shifts p' upward instead of subtracting the error bound for the lower side.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 8 "Confidence Intervals", section 8.3 A Population Proportion_
Related questions
A campus survey wants to estimate, with 95% confidence and a margin of error no greater thIn a Zogby poll of 48 respondents, nine rated a terrorist attack in their community as likOf 511 southern California homes surveyed for earthquake preparedness, 338 did NOT meet miContinuing the Field Poll example, p' = 0.79 from 400 of 506 surveyed. For a 90% confidencA Field Poll finds that 400 out of 506 surveyed California adults, about 79%, feel educatiAt the Ice Chalet, a randomly selected beginning skating class of 80 children has 64 girlsA poll of 1,200 voters finds 65% name the economy as the most significant election issue. A survey of 200 households finds that in 120 of them, the woman makes the majority of purc