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- Statistics 2
This half course requires the student to develop the concepts introduced in Statistics 1 of measurement and hypothesis testing.
- Set theory: the basics Axiomatic definition of probability
- Classical probability and counting rules
- Conditional probability and Bayes’ theorem.
- Discrete random variables
- Continuous random variables.
Common distributions of random variables:
- Common discrete distributions
- Common continuous distributions.
Multivariate random variables:
- Joint probability functions
- Conditional distributions
- Covariance and correlation
- Independent random variables
- Sums and products of random variables.
- Sampling distributions of statistics: Random samples
- Statistics and their sampling distributions
Sampling distribution of a statistic
- Sample mean from a normal population
- The central limit theorem Some common sampling distributions
- Prelude to statistical inference.
- Estimation criteria: bias, variance and mean squared error
- Method of moments estimation
- Least squares estimation
- Maximum likelihood estimation.
- Interval estimation for means of normal distributions
- Use of the chi-squared distribution
- Confidence intervals for normal variances.
- Setting p-value, significance level, test statistic t tests
- General approach to statistical tests
- Two type of error
- Tests for normal variances
- Comparing two normal means with paired observations
- Comparing two normal means
- Tests for correlation coefficients
- Tests for the ratio of two normal variances
Analysis of variance:
- One-way analysis of variance
- Two-way analysis of variance.
- Simple linear regression Inference for parameters in normal regression models;
- Regression ANOVA;
- Confidence intervals for E(y);
- Prediction intervals for y;
- Multiple linear regression models
If you complete the course successfully, you should be able to:
- Apply and be competent users of standard statistical operators and be able to recall a variety of well-known distributions and their respective moments
- Explain the fundamentals of statistical inference and apply these principles to justify the use of an appropriate model and perform tests in a number of different settings
- Demonstrate understanding that statistical techniques are based on assumptions and the plausibility of such assumptions must be investigated when analysing real problems.
- Newbold, P., W. Carlson and B. Thorne. Statistics for Business and Economics. London: Pearson.