The course starts with a review of some topics from probability theory e.g. moments and moment generating functions. It then launches into sampling theory with consideration of distributions related to the normal distribution viz t, Chi-square and F. Emphasis is on parameter estimation and hypothesis testing with applications. Methods of point and interval estimation and properties of estimators are considered. In the last part of the course Chi-square tests for goodness of fit and for independence as well as the Fisher’s exact test are considered with applications to data. Finally an introduction to linear regression analysis is given.
By the end of this course students should be able to: · Differentiate between parametric and non-parametric statistical inference.· State the properties of various discrete and continuous distributions.· Derive distributions of the sample mean and sum of random variables using the moment generating function technique.· Derive the t, Chi-square and F distributions and state their usefulness in sampling theory.· Calculate point and interval estimates of parameters.· Assess whether estimators satisfy the properties of good estimators.· Perform hypothesis tests with applications.· Apply the acquired tools to real life data by making inferences about properties of the distribution where the data is thought to have been drawn and to determine the likelihood that the distribution is the correct one.· Test for goodness of fit using the chi-square test.· Test for independence of variables using the chi-square test and fisher's exact test.· Use a statistical package e.g. S-Plus and/or R for data analysis particularly regression analysis.· Fit a simple linear regression model and interpret the results.· Perform non-parametric statistical inference.
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