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H-SC MATH 121 - Lecture 35 - Student's t Distribution Section 10.2

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IntroductionThe Decision TreeThe t-Test on the TI-83Testing for NormalityAssignmentStudent’s t DistributionLecture 35Section 10.2Robb T. KoetherHampden-Sydney CollegeWed, Mar 24, 2010Robb T. Koether (Hampden-Sydney College) Student’s t Distribution Wed, Mar 24, 2010 1 / 32Outline1Introduction2The Decision Tree3The t-Test on the TI-834Testing for Normality5AssignmentRobb T. Koether (Hampden-Sydney College) Student’s t Distribution Wed, Mar 24, 2010 2 / 32Outline1Introduction2The Decision Tree3The t-Test on the TI-834Testing for Normality5AssignmentRobb T. Koether (Hampden-Sydney College) Student’s t Distribution Wed, Mar 24, 2010 3 / 32IntroductionWe now have three different tests of hypotheses:I1-sample z-test of proportions (1-PropZTest).I1-sample z-test of means (Z-Test).I1-sample t-test of means (T-Test).We need to be careful when deciding which test to use.It takes practice.Robb T. Koether (Hampden-Sydney College) Student’s t Distribution Wed, Mar 24, 2010 4 / 32IntroductionWe now have three different tests of hypotheses:I1-sample z-test of proportions (1-PropZTest).I1-sample z-test of means (Z-Test).I1-sample t-test of means (T-Test).We need to be careful when deciding which test to use.It takes practice.Robb T. Koether (Hampden-Sydney College) Student’s t Distribution Wed, Mar 24, 2010 4 / 32IntroductionWe now have three different tests of hypotheses:I1-sample z-test of proportions (1-PropZTest).I1-sample z-test of means (Z-Test).I1-sample t-test of means (T-Test).We need to be careful when deciding which test to use.It takes practice.Robb T. Koether (Hampden-Sydney College) Student’s t Distribution Wed, Mar 24, 2010 4 / 32IntroductionWe now have three different tests of hypotheses:I1-sample z-test of proportions (1-PropZTest).I1-sample z-test of means (Z-Test).I1-sample t-test of means (T-Test).We need to be careful when deciding which test to use.It takes practice.Robb T. Koether (Hampden-Sydney College) Student’s t Distribution Wed, Mar 24, 2010 4 / 32IntroductionWe now have three different tests of hypotheses:I1-sample z-test of proportions (1-PropZTest).I1-sample z-test of means (Z-Test).I1-sample t-test of means (T-Test).We need to be careful when deciding which test to use.It takes practice.Robb T. Koether (Hampden-Sydney College) Student’s t Distribution Wed, Mar 24, 2010 4 / 32IntroductionWe now have three different tests of hypotheses:I1-sample z-test of proportions (1-PropZTest).I1-sample z-test of means (Z-Test).I1-sample t-test of means (T-Test).We need to be careful when deciding which test to use.It takes practice.Robb T. Koether (Hampden-Sydney College) Student’s t Distribution Wed, Mar 24, 2010 4 / 32Outline1Introduction2The Decision Tree3The t-Test on the TI-834Testing for Normality5AssignmentRobb T. Koether (Hampden-Sydney College) Student’s t Distribution Wed, Mar 24, 2010 5 / 32The Decision TreenXZ/σµ−=nXZ/σµ−≈Is σ known?Is the populationnormal?noyesnoyesIs n ≥ 30?noyesGive upCome backlaterRobb T. Koether (Hampden-Sydney College) Student’s t Distribution Wed, Mar 24, 2010 6 / 32The Decision TreenXZ/σµ−=nXZ/σµ−≈Is σ known?Is the populationnormal?noyesnoyesIs n ≥ 30?noyesGive upIs the populationnormal?noyesRobb T. Koether (Hampden-Sydney College) Student’s t Distribution Wed, Mar 24, 2010 6 / 32The Decision TreenXZ/σµ−=nXZ/σµ−≈Is σ known?Is the populationnormal?noyesnoyesIs n ≥ 30?noyesGive upIs the populationnormal?noyesIs n ≥ 30?noyesRobb T. Koether (Hampden-Sydney College) Student’s t Distribution Wed, Mar 24, 2010 6 / 32The Decision TreenXZ/σµ−=nXZ/σµ−≈Is σ known?Is the populationnormal?noyesnoyesIs n ≥ 30?noyesGive upTZnsXT≈−=/µIs the populationnormal?noyesIs n ≥ 30?noyesRobb T. Koether (Hampden-Sydney College) Student’s t Distribution Wed, Mar 24, 2010 6 / 32The Decision TreenXZ/σµ−=nXZ/σµ−≈Is σ known?Is the populationnormal?noyesnoyesIs n ≥ 30?noyesGive upTZnsXT≈−=/µnsXT/µ−=Is the populationnormal?noyesIs n ≥ 30?noyesRobb T. Koether (Hampden-Sydney College) Student’s t Distribution Wed, Mar 24, 2010 6 / 32The Decision TreenXZ/σµ−=nXZ/σµ−≈Is σ known?Is the populationnormal?noyesnoyesIs n ≥ 30?noyesGive upTZnsXT≈−=/µnsXT/µ−=Is the populationnormal?noyesIs n ≥ 30?noyesIs n ≥ 30?noyesRobb T. Koether (Hampden-Sydney College) Student’s t Distribution Wed, Mar 24, 2010 6 / 32The Decision TreenXZ/σµ−=nXZ/σµ−≈Is σ known?Is the populationnormal?noyesnoyesIs n ≥ 30?noyesGive upyesTZnsXT≈−=/µnsXT/µ−=nXZ/sµ−≈Is the populationnormal?noyesIs n ≥ 30?noyesIs n ≥ 30?noyesRobb T. Koether (Hampden-Sydney College) Student’s t Distribution Wed, Mar 24, 2010 6 / 32The Decision TreenXZ/σµ−=nXZ/σµ−≈Is σ known?Is the populationnormal?noyesnoyesIs n ≥ 30?noyesGive upyesTZnsXT≈−=/µnsXT/µ−=nXZ/sµ−≈Is the populationnormal?noyesIs n ≥ 30?noyesIs n ≥ 30?noyesGive upRobb T. Koether (Hampden-Sydney College) Student’s t Distribution Wed, Mar 24, 2010 6 / 32When to Use ZWhich statistic?Use z when σ is known and the population is normal (no matter howsmall the sample).Robb T. Koether (Hampden-Sydney College) Student’s t Distribution Wed, Mar 24, 2010 7 / 32When to Use ZnXZ/σµ−=nXZ/σµ−≈Is σ known?Is the populationnormal?noyesnoyesIs n ≥ 30?noyesGive upyesTZnsXT≈−=/µnsXT/µ−=nXZ/sµ−≈Is the populationnormal?noyesIs n ≥ 30?noyesIs n ≥ 30?noyesGive upRobb T. Koether (Hampden-Sydney College) Student’s t Distribution Wed, Mar 24, 2010 8 / 32When to Use ZWhich statistic?Use z when the population is not normal, but the sample size is large(whether or not σ is known).Robb T. Koether (Hampden-Sydney College) Student’s t Distribution Wed, Mar 24, 2010 9 / 32When to Use ZnXZ/σµ−=nXZ/σµ−≈Is σ known?Is the populationnormal?noyesnoyesIs n ≥ 30?noyesGive upyesTZnsXT≈−=/µnsXT/µ−=nXZ/sµ−≈Is the populationnormal?noyesIs n ≥ 30?noyesIs n ≥ 30?noyesGive upRobb T. Koether (Hampden-Sydney College) Student’s t Distribution Wed, Mar 24, 2010 10 / 32When to Use tWhich statistic?Use t when σ is not known and the population is normal (no matterhow large or small the sample).If the sample size is small, then we must use t.If the sample size is large, then we may use z instead of t.Robb T. Koether (Hampden-Sydney College) Student’s t Distribution Wed, Mar 24, 2010 11 / 32When to Use tnXZ/σµ−=nXZ/σµ−≈Is σ known?Is the


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H-SC MATH 121 - Lecture 35 - Student's t Distribution Section 10.2

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