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1 CLASS TOPICS 1 Ca’ Foscari University of Venice SYLLABUS OF STATISTICS 6C 2014-15 Prof. M. Romanazzi March 14, 2015 1 Class Topics References are given in parentheses. 1.1 Data analysis Frequency distributions Summarizing data by frequency tables. Notion of mode. Categorical and numerical data. Stem-and-leaf presentation. Grouping numerical data into intervals. Frequency vs density. Histogram as a density curve diagram. Shape of frequency distributions. Some common shapes: unimodal vs bimodal, symmetric vs asymmetric, increasing vs decreasing, uniform, normal. Interpreting shape. (Ross, Ch. 2 and 3) Quantiles and boxplot Sample quantiles. More specific examples: minimum and maximum, range and inter-quantile range, median and quartiles. Box-and-whiskers plot. Tukey’s outlier labeling rule. (Ross, Ch. 3) Mean, standard deviation and the normal curve Describing location and dispersion. Unimodal and symmetric distributions: mean, variance and standard deviation. Interpreting mean and standard deviation. Mean and standard deviation vs quantiles. Normal distributions. Areas of central intervals under the normal curve. Assessing accuracy of normal approximation to empirical histograms. (Ross, Ch. 3) Scatter plots and linear correlation coefficient Bivariate numerical data. Using scatter plots to graphically assess the features of joint distributions: location, dispersion, shape. Covariance and linear correlation coefficient. Using the linear correlation coefficient as a diagnostic of the strength of linear relationship (Ross, Ch. 2 and 3) Least squares line Fitting a line to bivariate data. Predicted values of the response variable and errors. Estimates of the coefficients by minimization of the sum of squared errors. Coefficient of determination. Role of linear correlation coefficient. (Ross, Ch. 12: 12.1 - 12.3, 12.8, 12.9) Suggested exercises: Ch. 2 (review section): 1-4, 8, 9, 12, 14, 16; Ch. 3 (review section): 2, 6, 8, 12, 13; Ch. 12.2: 3-5, Ch. 12.3: 8, 10, 12, 13, 15, Ch. 12.8: 1, 3 (except part d.), 6 (except part d.), Ch. 12.9: 1-5. Probability theory, random variables and probability distributions, summaries of probability distributions (expectation, variance and standard deviation, percentiles) and basic probability models (binomial, hypergeometric, normal) are required for the second part of the course. (Ross, Ch. 4, 5, 6) 1.2 Probability distribution of sample statistics Random sampling. The standard model of analysis of random variables associated to random sampling. Basic sample statistics: sample average and sample proportion, sample variance and sample standard deviation. Expectation and variance of basic statistics. Finding the probability distribution of a sample 2 TEXTBOOKS 2 statistic. Exact vs asymptotic distribution. Central limit theorem. Asymptotic normality. Law of large numbers. (Ross, Ch. 7) Suggested exercises: Ch. 7 (review section): 1-6, 9, 11, 12. 1.3 Estimation Estimation of the population mean and the population proportion. Using the (plug-in) standard error to evaluate the sampling error. Unbiased estimators. Confidence intervals for the population mean and the population proportion. t distribution. Comparing t distribution to standard normal distribution. Using t percentiles to obtain confidence intervals for the population mean of normal data. (Ross, Ch. 8. Lower and upper confidence intervals can be omitted. ) Suggested exercises: Ch. 8 (review section): 3-9, 12-15. 1.4 Test of hypotheses Statistical hypotheses and test statistics. Decisional approach, type 1 and type 2 errors, partition of the sample space into rejection region and its complement. The approach based on p-value. One - sided and two - sided tests of population mean. One - sided and two - sided tests of population proportion. (Ross, Ch. 9) Suggested exercises: Ch. 9.4: 1-4, 6, 12, Ch. 9.5: 1-3, 5, 8, 9, 12, 14, Ch. 9 (review section): 2, 5, 6, 14. 2 Textbooks Reference textbook is Ross, Sheldon M., Introductory Statistics, 2nd edition, Elsevier, 2005 (or more recent editions).