Slide 1Parameter estimationConfidence intervalsConfidence intervalsConfidence intervalsConfidence intervalsHypothesis TestingHypothesis TestingInference about varianceGoodness of fit testsNon-parametric testsregressionPROBABILITY AND STATISTICS IN COMPUTER SCIENCE AND SOFTWARE ENGINEERING Final Review1PARAMETER ESTIMATIONMethod of Moments:Understand what the method of moments is, and how it is usedYou will not likely have to use it – just understand how it worksKnow the difference between population and sample moments, and what the central moments areUnderstand how the method worksMethod of Maximum Likelihood:Same points – understand how it is used, why it works, how to apply itYou will not be asked to use it to do a computationStandard Error estimation – know what the standard errors are for common estimators (like sample mean). 2CONFIDENCE INTERVALSUnderstand the definition of what a confidence interval is and what it is notThe estimated parameter is either in the confidence interval or it is not 95% confidence interval means that if we create 100 confidence intervals of this type, approximately 95 of them will contain the parameterUnderstand how these are constructed, what the relationship is to the standard error of the estimator and the z- or t-parameter being usedCommon z-values will be givenKnow how to construct confidence intervals – e.g. for a sample mean3CONFIDENCE INTERVALSKnow how to construct confidence intervals for the difference of two meansUnderstand the definition of the margin of the confidence interval, and how it is computedUnderstand how to select the sample size large enough to ensure a certain marginKnow how to create confidence intervals in the case that the standard deviation of the population is unknownHow to estimate the standard deviation for large sample size n4CONFIDENCE INTERVALSKnow how to construct confidence intervals for population proportionsThe formula will be given, but know what it means and how to use itAlso know how to create a confidence interval for the difference in population proportionsKnow what to do when the standard deviation is unknown and the sample size is large: approximate the standard deviation by an estimatorCan use a z-statistic in this case5CONFIDENCE INTERVALSWhat to do when the standard deviation is unknown and the sample size is not large enoughMust use a t-distributionKnow how to do this for sample meansKnow how to create confidence intervals for the difference between two population means when the variance is unknown and the samples are not large enoughMethod one – pooled sample, if suspect the variances are equalMethod two – Satterwaithe approximation, if we suspect the variances are not equal6HYPOTHESIS TESTINGKnow how to formulate a hypothesis test, with a null hypothesis and alternative hypothesisUnderstand the difference between two-sided and one-sided (right-tailed and left-tailed) alternativesKnow the what Type I and Type II errors are, and why they are importantUnderstand what the significance level () of a hypothesis test is•D7HYPOTHESIS TESTINGKnow how to conduct a level - hypothesis testHow to formulate the null and alternative hypothesesHow to identify the accept and reject regionsHow to compute the test statistic for sample means or proportionsHow to draw conclusionsMake sure you can do this for both z- and t-distributionsP-valuesKnow how to compute themKnow how they relate to hypothesis testsUnderstand the concept behind them•D8INFERENCE ABOUT VARIANCEKnow how to create confidence intervals for population varianceKnow how to create hypothesis tests and how to compute p-values for a population varianceKnow how to use the chi-squared distributionKnow how to compare two population variances using an F-test and F distributionKnow how to do hypothesis tests, create confidence intervals for the ratio of the variances9GOODNESS OF FIT TESTSKnow how to use the chi-squared statistic to do a goodness of fit test for a particular distribution on data setAlso know how to do goodness of fit tests for an entire family of distributionsKnow how to apply this statistic to check independence of two variables10NON-PARAMETRIC TESTSKnow what the sign test is an how to apply itKnow what the Wilcoxon signed rank test is and how to applyKnow what the Mann-Whitney-Wilcoxon test is and how to applyUnderstand the concept behind the Bootstrap method, and why it is usedKnow the terminology and how a Bootstrap method is appliedUnderstand the concept behind Bayesian inference, and why it worksDon’t memorize derivationsDon’t need to be able to apply11REGRESSIONUnderstand the fundamental assumptions and concept behind lineast squares fittingUnderstand the fundamental idea behind linear regressionUnderstand the key ideas behind ANOVA, and why comparison of variance worksBe able to complete an ANOVA
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