Lecture12

# Lecture12 - Assignment After this lecture, start Assignment...

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1 Assignment • After this lecture, start Assignment #5. It’s in the course binder.

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2 Lecture 12 Comparison and control: The difference between two means
3 Overview • You can already calculate and interpret  confidence intervals hypothesis tests • for a single population mean μ Y e.g., average weight gain for college freshmen • Today you’ll learn the same thing for the difference between two population means ( μ Y1 μ Y2 ) e.g., difference between – average weight gain for college freshmen (Y 1 ) – average weight gain for college freshwomen (Y 2 ) • You’ll also learn how to use a  control group  as a comparison

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4 Topic: College weight gain • Tufts [University] Longitudinal Health  Survey collects weights at beginning and end of freshman year average gain: 5.25 pounds women’s average: 4.5 pounds men’s average: 6 pounds
5 Claim #1:  Freshmen gain more than freshwomen • Comparing two means: Today’s topic • Population 1: freshmen variable 1 (Y 1 ): change in their weight • Population 2: fresh women variable 2 (Y 2 ): change in their weight • We want to know about μ Y1 - μ Y2 the difference in average weight change between the population of freshmen and the population of freshwomen

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6 Difference between two means:  Point estimate and hypotheses • We’re interested in μ Y1 μ Y2 . • What’s a  point estimate  for this quantity? • Claim: “Men gain more than women.” Notate the pertinent hypotheses:
7 Difference between two means:  Point estimate and hypotheses • Given: mean weight gains for samples of men  and women. Ybar 1 , Ybar 2 • To test hypotheses, and get a confidence interval, what else do you need?

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8 Comparison of formulas 1 freedom of degrees 1 error standard test hypothesis interval confidence estimate point mean single a For 2 - = = - = ± N N S N S S S Y t tS Y Y Y Y Y Y Y Y Y μ ) 1 ( ) 1 ( ) 1 ( ) 1 ( variance" pooled " 2 ) 1 ( ) 1 ( freedom of degrees 1 1 error standard 0 : H if ) ( ) ( test hypothesis ) ( interval confidence estimate point means between difference a For 2 1 2 2 2 1 2 2 1 2 1 2 1 2 0 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 - + - - + - = - + = - + - + = = - - = - - - = ± - - - - - - - N N S N S N S N N N N N N S S S Y Y S Y Y t tS Y Y Y Y Y Y pooled pooled Y Y Y Y Y Y Y Y Y Y Y Y Y Y
9 Steps of a hypothesis test (review) 1. State null and research hypotheses 2. Collect sample 3. Calculate test statistic 4. If the null hypothesis were true, how extreme/unusual would the test statistic be?

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Lecture12 - Assignment After this lecture, start Assignment...

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