Slide 1OverviewOverviewOverviewPROBABILITY AND STATISTICS IN COMPUTER SCIENCE AND SOFTWARE ENGINEERING Chapter 9: Statistical Inference1OVERVIEWLast time, we explored the basics of hypothesis testing.We saw how to construct null and alternative hypothesis, how to construct test statistics, and (based upon sample data) either reject or accept the null hypothesis with some level of significance We looked at situations when the test statistic was a standard normal variable …Sample mean, drawn from a normally distributed population Sample mean, with large sample size (any population distribution)Sample proportion, with large sample sizeDifferences between means and proportions under these situationsWe noted the difference between one-sample and two-sample tests (comparing statistics from two different samples)•:2OVERVIEWWe saw what to do if the variance was unknown and the sample size was not large enough to assume a Z-Test – here we use the T-Test, which involves the Student’s t-distributionNotice that this still assumed that the distribution of the estimator is normal, e.g. sample mean from normally distributed population with small sample sizeWe saw that if we were doing a two-sample tests and we could assume that the variances were equal, we could estimate the variance by pooling the data•:3OVERVIEWIn this lecture, we will look at the connection between hypothesis tests and confidence intervals, and see that they are basically the same conceptWe will then turn this problem around and look at it a different way …We’ll investigate the choice of , the level of significance for the testWe’ll see how we can create P-values, which allow us to analyze the sample data for any value of and draw conclusionsWe will see that, given an observed test statistic, the P-value is related to the probably that we will observe this statistic if the Null Hypothesis is trueIn some sense, this allows us to use the observed sample to draw a conclusion about the smallest/largest that would make sense in this
View Full Document