STAT211 Chapter Notes - Chapter 10: Confidence Interval
26 Jun 2018
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Chapter 10
u1 – u2 : The difference between two population means. Estimated by x̄1 - x̄2.
Confidence Interval for the Difference in two population means (o is known):
(x̄1 - x̄2) +/- za/2 * √(o12/n1 + o22/n2)
Test Statistic: Z = (x̄1 - x̄2) / √(o12/n1 + o22/n2)
Pooling Sample Variances: sp2 = [s12(n1 – 1) + s22(n2 – 1)] / (n1 + n2 – 2)
Pooled T-Procedure Confidence Interval for the Difference in two population means:
(x̄1 - x̄2) +/- ta/2 * sp * √(1/n1 + 1/n2)
Pooled T-Procedure Test Statistic: t = (x̄1 - x̄2) / [sp * √(1/n1 + 1/n2)]
DF for Pooled T-procedure: n1 + n2 – 2
Welch Confidence Interval for the Difference in two population means:
(x̄1 - x̄2) +/- ta/2 * √(s12/n1 + s22/n2)
Welch Test Statistic: t = (x̄1 - x̄2) / √(s12/n1 + s22/n2)
Paired Difference Procedure: When samples are dependent (eg same sample subject is
tested before and after and the difference is of interest).
Paired Confidence Interval: (x̄ - u0) +/- ta/2 * s/√n
Paired Test Statistic: t = (x̄ - u0) / ( s/√n)
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Document Summary
Chapter 10 u1 u2 : the difference between two population means. Confidence interval for the difference in two population means (o is known): (x 1 - x 2) +/- za/2 * (o1. Test statistic: z = (x 1 - x 2) / (o1. 2(n2 1)] / (n1 + n2 2) Pooled t-procedure confidence interval for the difference in two population means: (x 1 - x 2) +/- ta/2 * sp * (1/n1 + 1/n2) Pooled t-procedure test statistic: t = (x 1 - x 2) / [sp * (1/n1 + 1/n2)] Df for pooled t-procedure: n1 + n2 2. Welch confidence interval for the difference in two population means: (x 1 - x 2) +/- ta/2 * (s1. Welch test statistic: t = (x 1 - x 2) / (s1. Paired difference procedure: when samples are dependent (eg same sample subject is tested before and after and the difference is of interest).
