Duration: 3 hours for 13 weeks [ECTS: 6]

COURSE DESCRIPTION

1. Descriptive Statistics: Samples and population, Percentiles and Quartiles, Measures of central tendency and variability, Grouped data and frequency distributions, Histogram and the polygon line, Skewness and kurtosis, Chebyshev’s theorem, Methods of displaying the data, Pie and bar charts, Box plots.
2. Probability: Random experiment, Elementary outcome, Sample space and events, Classical definition of probability, Probability as the limit of relative frequency, Subjective probability, Axioms and rules for probability, Conditional probability, Joint and marginal probabilities, Independent events, The law of total probability and Bayes’ theorem.
3. Random variables: Discrete random variables, Probability distribution and cumulative distribution function, Expected value and standard deviation of a random variable, Bernoulli and Binomial random variables, The Poisson distribution, The negative Binomial Distribution, The Geometric and Hypergeometric distribution, Continuous random variables, Probability density function, The Uniform and Exponential distributions.
4. The Normal distribution: Properties of the Normal distribution, The Standard Normal distribution, Finding probabilities of the Standard Normal distribution, Transforming a Normal random variable to the Standard Normal, The inverse transformation, Normal approximation of Binomial and Poisson distributions.
5. Sampling distributions: Sample statistics as estimators of population parameters, Sampling distribution of the sample mean, Central Limit Theorem, Student-t distribution, Sampling distribution of the variance, Chi-squared and F distributions.
6. Confidence intervals: Confidence intervals for the population mean when the population variance is known and unknown, Confidence intervals for the population proportion, Confidence intervals for the population variance.
7. Hypothesis testing: The Null and Alternative hypotheses, Significance level, Type I and II errors, Power of the test, Hypothesis testing for the population mean, the population variance and the population proportion.

LEARNING OUTCOMES

By the end of this course, students will be able to:

1. Know and understand basic statistical concepts in order to be able to distinguish the difference between populations and samples, quantitative and qualitative variables, census and sample surveys, representativeness and accuracy, sampling and non-sampling errors,
2. Construct frequency distributions and calculate/interpret/analyze statistical parameters of central tendency, location, and dispersion,
3. Identify the sample space of a random experiment and then identify/calculate marginal and conditional probabilities and apply the theorems of total probability and Bayes,
4. Understand the differences between discrete and continuous random variables, construct probability distributions for discrete random variables, compute cumulative distribution functions, and calculate the expected values and variances,
5. Realize the properties of normal distributions so that by transforming them to the standard normal distribution to calculate/analyze probabilities using the statistical tables, while at the same time being able to formulate business problems and applying the inverse Normal transformation to determine requested values of percentiles and parameters,
6. Understand the differences between population parameters and sample statistics, so that by applying the central limit theorem to construct/analyze confidence intervals for population means, population proportions and population variance, as well as, to assess the validity of results obtained,
7. Understand the business problem in order to correctly formulate the null and alternative hypothesis, carry out the appropriate test of hypotheses either using appropriate sample statistics at given levels of significance or using the p-value and assess the validity of the results obtained,

8. Carry out the required descriptive and inductive statistical analysis using appropriate statistical software