Cheat Sheet for Confidence Intervalsannegloag.weebly.com/.../9/...confidence_intervals.pdf ·...
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Cheat Sheet for Confidence Intervals CI for Sample Statistic Formula Use When One population mean, ± ! is known x is normal or ≥ 30 One population mean, ± ! = − 1 < 30 or is unknown One population proportion, p ± ! ≥ 10 ≥ 10 One population variance, ! ! − 1 ! ! ! < ! < − 1 ! ! ! = − 1 x is normal One population standard deviation, − 1 ! ! ! < < − 1 ! ! ! = − 1 x is normal Difference of two population means ( ! − ! ) ! − ! ( ! − ! ) ± ! ! ! ! + ! ! ! ! , ! are known x is normal or ! , ! ≥ 30 Difference of two population means ( ! − ! ) ! − ! ( ! − ! ) ± ! ! ! ! + ! ! ! ! , ! are unknown or ! , ! < 30 = ! ! / ! + ! ! / ! ! ( ! ! / ! ) ! ! − 1 + ( ! ! / ! ) ! ! − 1 Difference of two proportions ( ! − ! ) ! − ! ( ! − ! ) ± ! ! ! ! + ! ! ! ! ! ≥ 10; ! ! ≥ 10 ! ! ≥ 10; ! ! ≥ 10 Critical zvalues: Confidence Level ! 90% 1.645 95% 1.96 98% 2.33 99% 2.575 Critical tvalues/ ! (on the back)
Transcript of Cheat Sheet for Confidence Intervalsannegloag.weebly.com/.../9/...confidence_intervals.pdf ·...
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
