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Principle of Economics and Statistics - unit 2
Code: G290JB
Teacher:  Achille Vernizzi
Year: 
Term: 
CFU: 
CFU subdivision: Lectures: 1
Practices in classroom: 1
Basic aims:  The aim of the course is to introduce students to jargon and basic principles of economics and statistical sciences. The module of Economics is meant to explain laws describing behaviour and interaction among economic agents (families and firms) mainly at micro level (microeconomics) with a short outline at aggregated level (macroeconomics). The module of statistics introduces descriptive statistics and treats some topics of inferential statistics.
Acquired skills:  Students should be able to understand economic information (about production, consumption and food markets dynamic) presented both on newspapers and reviews of food science. Students should be able to correctly understand and represent statistical data both in tabular and graphical form.
Course contents:  The Language Of Statistics
Graphical Representation Of Data
Numerical Description Of Data
Bivariate Data Analysis
Probability
Random Variables And Probability Distributions
Sampling Distributions And Confidence Intervals
Principles Of Hypothesis Testing
Test On A Single Population
Program:  The Language Of Statistics
Graphical Representation Of Data
Numerical Description Of Data
Bivariate Data Analysis
Probability
Random Variables And Probability Distributions
Sampling Distributions And Confidence Intervals
Principles Of Hypothesis Testing
Test On A Single Population
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Definition of Statistics. Population, sample and variables. Difference between parameter and statistic. Factors affecting sample size. Sample choice: the simple random sample. Data types: qualitative (nominal and ordinal) and quantitative (discrete and continuous). Difference between descriptive and inferential statistic. The summation operator.
Frequency distribution or frequency table: absolute frequencies, relative frequencies, cumulative relative frequencies. The continuous case: choice of the number and width of classes; classes of different width, density. Graphical representations: pie chart, bar plot, stick plot, histogram.
Measures of central tendency. Mode. Median. Arithmetic mean (simple and weighted for frequency tables). Simmetry/asymmetry of a distribution.
Measures of dispersion: range, variance, mean square deviation. Empirical rule for bell-shaped distributions. Measures of relative dispersion: the coefficient of variation. z scores. Measures of relative tendency: percentiles and quartiles (for raw data and frequency tables). Interquartile deviation.
Bivariate analysis. Analysis of bivariate qualitative data: contingency table; joint absolute and relative frequencies; graphical representation through grouped bar chart.
Analysis of bivariate quantitative data: scatter plot; types of relationship between two variables; linear correlation coefficient; regression or least squares line: computation and interpretation of parameters; interpolation and extrapolation of values.
Random experiment. Sample space. Random event. Probability: classical definition. Complementary event. Intersection and union of two events. Incompatible events. General rule for the computation of the probability of the union of two events. Conditional probability. Independent events.
Definition of random variable. Discrete random variables. Probability function and graphical representation. Expected vale and variance. Bernoulli random variable. Binomial random variable.
Continuous random variables. Probability density function. Normal random variable and meaning of its parameters. Standardization of a random variable and standard normal variable. Z tables. Computation of probabilities for intervals. Computation of quantiles.
Sample distributions. Distribution of the sample mean: expected value and standard error. Central limit theorem. Distribution of the sample mean for normal variable. Point and interval estimators.
Confidence intervals: definition. Confidence interval for the mean: normal population and standard deviation known; normal population and standard deviation unknown; Student's T random variable. Interpretation of a confidence interval. Width of a confidence interval and relationship between sample size, confidence level and standard deviation. Confidence interval for a proportion.
Hypothesis test. General principles. Stages of hypothesis testing. Test statistic, critical values and rejection region of a test. Test for the mean of a normal variable with known variance. Use of Z statistic. Test for the mean of a normal variable with unknown variance. Use of Student's T. Errors related to hypothesis test (first and second type).
Prerequisites:  THE COURSE WILL BE DELIVERED IN ITALIAL Knowledge of basic mathematics and analytical geometry.
Preparatory instructions:  Students are highly encouraged to attend the course and to study for the math exam "essentials of calculus". However having passed that exam is not a strict prerequisite for attending this course.
Learning materials:  Pelosi M. K., Sandifer T. M., Cerchiello P., Giudici P. (2009). Introduzione alla Statistica, McGraw-Hill.
Didactic resources are available on the Ariel web page:
http://ees.ariel.ctu.unimi.it/v3/home/Default.aspx
Other info:  The exam consists in a written test (IN ITALIAN) on the topics covered both in the economics and in the statistics classes. For each part (economics and statistics) students will face true/false questions, multiple choice questions and exercises. Wrong answers does not lead to negative score. The exam mark will be the sum of economics and statistics marks.
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Program of Principle of Economics and Statistics - unit 2 (pdf version)
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