MATH117_Lecture_Lock4-5 - Section 4.5 Confidence Intervals...

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Statistics: Unlocking the Power of DataLock5Section 4.5Confidence Intervals and Hypothesis Tests
Statistics: Unlocking the Power of DataLock5Bootstrap and Randomization DistributionsBootstrap DistributionRandomization DistributionOur best guess at the distribution of sample statisticsOur best guess at the distribution of sample statistics, if H0were trueCentered around the observed sample statisticCentered around the null hypothesized valueSimulate sampling from the population by resampling from the original sampleSimulate samples assuming H0were trueBig difference: a randomization distribution assumes H0is true, while a bootstrap distribution does not
Statistics: Unlocking the Power of DataLock5Which Distribution?
Which distribution below is the bootstrap distribution?
Statistics: Unlocking the Power of DataLock5
Which distribution is the randomization distribution?
Statistics: Unlocking the Power of DataLock5Body TemperatureWe created a bootstrap distribution for average body temperature by resampling with replacement from the original sample (
Statistics: Unlocking the Power of DataLock5Body TemperatureWe also created a randomization distribution to see if average body temperature differs from 98.6F by adding 0.34 to every value to make the null true, and then resampling with replacement from this modified sample:
Statistics: Unlocking the Power of DataLock5Body TemperatureThese two distributions are identical (up to random variation from simulation to simulation) except for the centerThe bootstrap distribution is centered around the sample statistic, 98.26, while the randomization distribution is centered around the null hypothesized value, 98.6The randomization distribution is equivalent to the bootstrap distribution, but shifted over
Statistics: Unlocking the Power of DataLock5Body TemperatureBootstrap DistributionRandomization DistributionH0: = 98.6Ha: ≠ 98.698.2698.6

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