Home › AP Statistics › Statistics › Confidence Intervals › A survey of 1,200 people finds 61% feel the pres…
A survey of 1,200 people finds 61% feel the president is doing an acceptable job. For a 90% confidence level, z(0.05)=1.645. What is the resulting confidence interval for the true proportion, rounded to two decimals?
A(0.59, 0.63)
B(0.50, 0.72)
C(0.61, 0.72)
D(0.39, 0.61)
Answer & Solution
Correct answer: A. (0.59, 0.63)
1. p' = 0.61, q' = 0.39, and n = 1,200.
2. EBP = 1.645*sqrt((0.61)(0.39)/1200) ≈ 1.645*0.01409 ≈ 0.02.
3. Lower bound: 0.61 - 0.02 = 0.59, and upper bound: 0.61 + 0.02 = 0.63.
4. Option C only shifts p' upward, so its lower bound is not correctly centered.
_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