Happiness comes not from material wealth but less desire.

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Inferences Comparing Two Population Means

Paired samplesIndependent samples

Estimation Tests- z test and t test

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Paired Samples

If the same set of sources are used to obtain data representing two populations, the two samples are called paired. The data might be paired:– As a result of the data from certain “before” and

“after” studies– From matching two subjects to form “matched

pairs”

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Tests for Paired Samples

Calculate the pair differences Proceed as in one sample case

Example: Figure 11.1

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Independent Samples

The two samples are unrelated

Example: Chapter 11, problem 15 (heart.mpj)

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Estimation for

Point estimator Confidence interval

1. Normal populations with known , or two large samples (n1,n2>30): Z interval

2. Normal populations with unknown t interval : pooled t interval : approximate t interval

3. At least one nonnormal population and at least one small sample: out of our scope

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Two Populations

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Tests for d0

1. Normal populations with known , or two large samples (n1,n2>30): Z test

2. Normal populations with unknown t test : pooled t test : approximate t test

3. At least one nonnormal population and at least one small sample: out of our scope

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Two Populations

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Minitab: stat>>basic statistics>>2 sample t …

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Results for: HEART.MTW Two-Sample T-Test and CI: pdi, trtment

Two-sample T for pdi

trtment N Mean StDev SE Mean 0 73 91.9 16.5 1.9 1 70 97.8 14.7 1.8

Difference = mu (0) - mu (1) Estimate for difference: -5.85 95% CI for difference: (-11.02, -0.68) T-Test of difference = 0 (vs not =): T-Value = -2.24 P-Value = 0.027 DF = 141 Both use Pooled StDev = 15.6318

Two-Sample T-Test and CI: pdi, trtment

Two-sample T for pdi

trtment N Mean StDev SE Mean 0 73 91.9 16.5 1.9 1 70 97.8 14.7 1.8

Difference = mu (0) - mu (1) Estimate for difference: -5.85 95% CI for difference: (-11.01, -0.70) T-Test of difference = 0 (vs not =): T-Value = -2.24 P-Value = 0.026 DF = 140

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