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# Hypothesis testing (5).docx

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McMaster University

Statistics

STATS 2B03

Aaron Childs

Fall

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October 23 , 2012
Stats 2B03: Statistical Methods for Science
Hypothesis Testing (5)
6.4 & 7.3 C.I. and Testing for a Difference in Two Means
- we are going to take independent random samples from two populations,
and we want to estimate μ -μ1an2 test one of
1. H A μ 1μ 2
2. H A μ 1μ 2
3. H A μ 1μ 2
Small sample results (n <10 or n <32)
- if 1 =σ 22
step 1: calculate
2
, where sp= is called the pooled
√
sample variance
step 2: same as index card, but replace z by . A 100(1-α)% CI
for μ1-μ2is X1avg-X2avg± √ ( )
⁄
assumptions:
the samples are independent
both populations must be normal
2 2
the population variances must be equal (σ =σ 1 2
- if 1 ≠σ 22
step 1: calculate
√
step 2: same as index card, but replace Z with t’ where
,
replace α by 1 – α in case I and II and by 1 - ⁄ in case III
A 100(1 – α)% confidence interval for μ -μ is

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