Transcription of Con dence intervals and hypothesis tests - mit.edu
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Con dence intervals and hypothesis tests - mit.edu
Chapter 2 Confidence intervals and hypothesis testsThis chapter focuses on how to draw conclusions about populations from sample data. We llstart by looking at binary data ( , polling), and learn how to estimate the true ratio of 1sand 0s with confidence intervals , and then test whether that ratio is significantly differentfrom some baseline value using hypothesis testing. Then, we ll extend what we ve learnedto continuous measurements. Binomial dataSuppose we re conducting a yes/no survey of a few randomly sampled people1, and we wantto use the results of our survey to determine the answers for the overall population. The estimatorThe obvious first choice is just the fraction of people who said yes. Formally, suppose wehavensamplesx1, .. ,xnthat can each be 0 or 1, and the probability that eachxiis 1isp(in frequentist style, we ll assumepis fixed but unknown: this is what we re interestedin finding). We ll assume our samples areindendepent and identically distributed ( ),meaning that each one has no dependence on any of the others, and they all have the sameprobabilitypof being 1.
Statistics for Research Projects Chapter 2 Since the expectation of ^pis equal to the true value of what ^pis trying to estimate (namely p), we say that ^pis an unbiased estimator for p.
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