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Cheat Sheet for Confidence Intervals
CI for Sample Statistic Formula Use When One population mean, 𝜇
𝑥
𝑥 ± 𝑧! 𝜎𝑛 𝜎 is known
x is normal or 𝑛 ≥ 30
One population mean, 𝜇
𝑥
𝑥 ± 𝑡! 𝑠𝑛
𝑑𝑓 = 𝑛 − 1
𝑛 < 30 or 𝜎 is unknown
One population proportion, p
𝑝 𝑝 ± 𝑧!
𝑝𝑞𝑛
𝑛𝑝 ≥ 10 𝑛𝑞 ≥ 10
One population variance, 𝜎!
𝑠!
𝑛 − 1 𝑠!
𝜒!!< 𝜎! <
𝑛 − 1 𝑠!
𝜒!!
𝑑𝑓 = 𝑛 − 1
x is normal
One population standard deviation, 𝜎
𝑠
𝑛 − 1 𝑠!
𝜒!!< 𝜎 < 𝑛 − 1 𝑠!
𝜒!!
𝑑𝑓 = 𝑛 − 1
x is normal
Difference of two population means (𝜇! − 𝜇!)
𝑥! − 𝑥! (𝑥! − 𝑥!) ± 𝑧!
𝜎!!
𝑛!+𝜎!!
𝑛!
𝜎!,𝜎! are known x is normal or 𝑛!,𝑛! ≥ 30
Difference of two population means (𝜇! − 𝜇!)
𝑥! − 𝑥! (𝑥! − 𝑥!) ± 𝑡!
𝑠!!
𝑛!+𝑠!!
𝑛!
𝜎!,𝜎! are unknown or 𝑛!,𝑛! < 30
𝑑𝑓 =𝑠!!/𝑛! + 𝑠!!/𝑛! !
(𝑠!!/𝑛!)!𝑛! − 1
+ (𝑠!!/𝑛!)!𝑛! − 1
Difference of two proportions (𝑝! − 𝑝!)
𝑝! − 𝑝! (𝑝! − 𝑝!)± 𝑧!
𝑝!𝑞!𝑛!
+𝑝!𝑞!𝑛!
𝑛!𝑝! ≥ 10; 𝑛!𝑞! ≥ 10 𝑛!𝑝! ≥ 10; 𝑛!𝑞! ≥ 10
Critical z-‐values: Confidence Level
𝑧!
90% 1.645 95% 1.96 98% 2.33 99% 2.575 Critical t-‐values/𝜒! (on the back)
Critical t-‐values
𝝌𝟐 Values For 𝝌𝑹𝟐 use
!!!!
For 𝝌𝑳𝟐 use !!!!
with df = n -‐ 1