Statistics

Course Description

COURSE CONTENT

• Descriptive statistics: Statistical variables. Tables and graphs. Central tendency measures. Variability measures. Location measures.
• Basics of probability theory: Probability space. Defining probability. Conditional probability. Independent events. Discrete and continuous random variables. Mathematical expectation and variance of a random variable. Binomial distribution. Hypergeometric distribution. Poisson distribution. Normal distribution.
• Testing statistical hypotheses and confidence intervals: Random sample. Point estimation of population mean and variance. Statistical test. Type I and II errors; power of a test. Test about population mean; t-test and large sample tests. Confidence interval for population mean; sample from a normal distribution and large sample. Two-sample t-test for comparison of means. F-test for equality of variances. Single factor ANOVA. Test of proportion. Confidence interval for proportion. Test for comparison of two proportions. χ²-tests for goodness-of-fit, independence and homogeneity.
• Linear regression model: Fitted line; the method of least squares. Confidence intervals for the linear regression parameters. Testing hypothesis about regression parameters. Prediction. Confidence intervals for predicted dependent variable and its mean value. Pearson’s correlation coefficient. Test for the significance of the correlation coefficient.

LEARNING OUTCOMES

• graphically represent the data (bar chart, histogram, pie chart, box-and-whisker diagram), and calculate measures of central tendency and variability, with and without a computer
• apply properties of probability and Laplace's model to calculate probabilities of random events
• explain the notion of discrete and continuous random variables and calculate their expectation and variance
• define and recognize the binomial, hypergeometric, Poisson and normal distribution, and calculate probabilities of random events based on these distributions
• determine confidence intervals for population mean and proportion
• apply appropriate statistical hypothesis test (test for a population mean, two-sample t-test for a difference in mean, F-test of equality of variances, one-way ANOVA, test of proportion and comparison of two proportions, χ²-tests for goodness-of-fit, independence and homogeneity) and correctly interpret the results, with or without a computer
• apply linear regression model and conduct statistical test related to the linear regression, with or without a computer

To enrol in this course, the following courses must be completed:

• Matemathics 1
• Matemathics 2
• Basic Informatics