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Happiness comes not from material wealth but less desire.

Happiness comes not from material wealth but less desire. Inferences Comparing Two Population Means. Paired samples Independent samples Estimation Tests- z test and t test. Paired Samples.

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Happiness comes not from material wealth but less desire.

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  1. Happiness comes not from material wealth but less desire.

  2. Inferences Comparing Two Population Means Paired samples Independent samples Estimation Tests- z test and t test

  3. 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”

  4. Tests for Paired Samples • Calculate the pair differences • Proceed as in one sample case Example: Figure 11.1

  5. Independent Samples • The two samples are unrelated • Example: Chapter 11, problem 15 (heart.mpj)

  6. Estimation for m1-m2 • Point estimator • Confidence interval • Normal populations with known s1,s2, or two large samples (n1,n2>30): Z interval • Normal populations with unknown s1,s2: t interval • s1=s2: pooled t interval • s1=s2: approximate t interval • At least one nonnormal population and at least one small sample: out of our scope

  7. Two Populations

  8. Tests for m1-m2 = d0 • Normal populations with known s1,s2, or two large samples (n1,n2>30): Z test • Normal populations with unknown s1,s2: t test • s1=s2: pooled t test • s1=s2: approximate t test • At least one nonnormal population and at least one small sample: out of our scope

  9. Two Populations

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

  11. 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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