ST104B Statistics 2 (half course)
There has been a minor revision to this syllabus.
Students may bring into the examination hall their own hand held electronic calculator. If calculators are used they must satisfy the requirements listed in Section 3, Assessment for the programme, of the Detailed Regulations.
Statistical tables will be provided.
ST1004B Statistics 2 must be taken after, or at the same time as, ST104A Statistics 1.
Random experiment, sample space, event; Complement, union, intersection; Probability and its axioms; conditional probability; independence; Law of total probability, Bayes' theorem; Permutations and combinations; Sampling without replacement
Random variables and distributions
Random variables; Discrete and continuous distributions; cumulative distribution function; Probability mass function; Common discrete distributions; Probability density function; Properties of continuous random variables; Common continuous distributions
Expectation and variance
Expectation; Expectation of a function; Properties of expectation; Variance; Expectation and variance of common distributions
Two random variables; Independence; Expected values; Covariance
Mean and variance of a sample mean; sampling for a normal population; The Central Limit Theorem
Intervals for the mean of a normal population; Intervals for mean differences; Confidence intervals for proportions; confidence intervals for variance
Hypotheses; Test statistics and critical regions; Type I and type II errors; Level and power; Testing hypotheses about population means; Link to Confidence Intervals; Two-sample tests; p-values; Tests for binomial probabilities of success; Testing hypotheses about population variances; One-sample test; Two-sample test
Analysis of variance
One-way analysis of variance; Confidence intervals and tests for population group means; Two-way analysis of variance; Tests for row effects and column effects; Confidence intervals; Fitted values and residuals; Sum of squares identity
Response variable and explanatory variable; Estimation of α and β: Sums of squares identity; Sample covariance and sample correlation
Simple linear regression
The model for linear regression; Means and variances of ˆα and ˆ β; Interval estimates for fitted values; Spotting difficulties
Correlation between two random variables; Regression and the coefficient of determination R2; Testing ρ = 0 for a bivariate normal distribution
The model for linear regression; Least squares fitting; Sum of squares identity; Coefficient of Determination; Computation; Extrapolation; Collinearity; Diagnostic Plots
Tests for goodness-of-fit
Basic counting model; A goodness-of-fit statistic; Testing when there are unknown parameters; Testing for association in two-way tables