# Stats 20 lecture23 on two sample testing - Stat 20 Intro to...

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Stat 20: Intro to Probability and StatisticsLecture 23: Two Sample TestingTessa L. Childers-DayUC Berkeley4 August 2014
RecapSurveysExperimentsRecap: Hypothesis TestingSteps in Hypothesis Testing:1State the hypothesesNull:The difference between the sample and the box is dueto chance errorAlternative:The difference between the sample and the boxis not due to chance error, but to the box being different2Gather evidence: SRS or repeated experimentation2 / 28
RecapSurveysExperimentsRecap: Hypothesis Testing (cont.)3Compare evidence to null hypothesis: Calculate a teststatistic, using observed and expected values4Decide whether or not to reject the null hypothesis: Calculatea p-value, measuring the strength of the evidence against thenull hypothesis. Values near 1 are weak evidence. Values near0 are strong evidence.3 / 28
RecapSurveysExperimentsBy the end of this lecture...You will be able to use hypothesis tests to compare 2 groups.4 / 28
RecapSurveysExperimentsThe Big (Academic) GameMuch is made of the Berkeley-Stanford rivalry, and academics areno exception. Imagine we are interested in seeing whether or notfreshmen from Stanford have higher SAT scores(reading+math+writing), since they are a private, Ivy Leagueuniversity. There are 4109 incoming freshmen at Cal. A SRS of400 students is taken from Cal, and found to have an average SATscore of 2050, and an SD of 600. There are 1704 incomingfreshmen at Stanford. A SRS of 100 students is taken fromStanford, and found to have an average SAT score of 2100, and anSD of 500.Draw a box model to illustrate this situation5 / 28
RecapSurveysExperimentsThe Big (Academic) Game (cont.)We know what the averages and SDs of the samples are. Usingthis, we can estimate the probability histograms for the average.Best guesses for probability histograms for avg:Berkeley SAT ScoreMath + Reading + WritingAverageDensity195020002050210021500.0000.0020.0040.0060.0080.0100.012Stanford SAT ScoreMath + Reading + WritingAverageDensity190020002100220023000.0000.0020.0040.0060.0086 / 28
RecapSurveysExperimentsThe Big (Academic) Game (cont.)But, we’re really interested in whether Stanford “wins” atacademics.Two curves seem differentAre they really different? Or isit just due to chance?SAT ScoreMath + Reading + WritingAverageDensity19502000205021002150220022500.0000.0020.0040.0060.0080.0100.012CalStanford7 / 28
RecapSurveysExperimentsThe Big (Academic) Game (cont.)Null Hypothesis:Difference is due to chanceDifference in population averages = 0avgcal-avgstan= 0Alternative Hypothesis:Difference isn’t due to chanceStanford’s average is higheravgcal-avgstan<08 / 28
RecapSurveysExperiments