Home › AP Statistics › Statistics › Confidence Intervals › A political action committee (PAC) sample of 30 …
A political action committee (PAC) sample of 30 gives x-bar = $251,854.23 and s = $521,130.41, so df = 29. For a 96% confidence level, t(0.02,29) = 2.150 gives EBM ≈ $204,561.66. What is the resulting confidence interval?
A($251,854.23, $456,415.89)
B($0.00, $521,130.41)
C($47,292.57, $456,415.89)
D($47,292.57, $251,854.23)
Answer & Solution
Correct answer: C. ($47,292.57, $456,415.89)
1. Subtract the error bound from x-bar: 251,854.23 - 204,561.66 = 47,292.57.
2. Add the error bound to x-bar: 251,854.23 + 204,561.66 = 456,415.89.
3. The 96% confidence interval for the mean amount raised is ($47,292.57, $456,415.89).
4. Options A and D each apply the error bound to only one side of x-bar, producing a lopsided, incorrect interval.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 8 "Confidence Intervals", section 8.2 A Single Population Mean using the Student t Distribution_
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