This activity investigates the assumption that older individuals are more likely to vote Conservative compared to younger individuals. Based on survey data from two age groups, students will test whether there is a statistically significant difference in voting preference using a proportion-based hypothesis test. Additionally, a confidence interval will be calculated to estimate the magnitude of the difference in support for the Conservative party between people over and under 40.

Seat Belt Usage and Serious Injury Risk in Car Accidents' This statistical exercise examines whether wearing a seat belt significantly reduces the likelihood of serious injury in car accidents among children. Using data collected from hospital admissions, students will apply hypothesis testing to compare injury rates between two groups: those who were wearing seat belts and those who were not. The task involves clearly formulating null and alternative hypotheses, calculating relevant proportions and test statistics, and drawing conclusions based on a 5% significance level to determine if the observed difference in injury severity is statistically significant.

Efficient Source Coding: Comparing Shannon-Fano and Huffman Algorithms This exercise explores two fundamental techniques in information theory used for source coding: the Shannon-Fano and Huffman algorithms. Students are given a discrete memoryless source with assigned symbol probabilities and tasked with constructing both types of codes. The goal is to analyze each method's efficiency by calculating average code lengths and comparing them to the theoretical entropy of the source. The activity highlights the distinctions between heuristic and optimal encoding strategies, reinforcing how information can be compressed effectively without loss.

Channel capacity represents the maximum amount of information that can be reliably transmitted over a communication channel. It is determined by the maximum mutual information between the input and output, optimized over all possible input probability distributions.

Data compression is driven by the need to enhance the efficiency of digital information processing.

Theory on the Kraft Inequality

Theory of Mutual Information in Information Theory

This exercise guides students through real-world applications of the normal distribution by examining the weight characteristics of Arab horses. Using statistical parameters—mean and standard deviation—students will compute probabilities of horses falling within certain weight ranges, determine interval likelihoods using symmetry and complement rules, and identify thresholds corresponding to specific percentile ranks. The problems reinforce core concepts in standardization (z-scores), cumulative probability, and distributional interpretation—all within an accessible, tangible scenario.

This exercise explores the statistical behavior of a game character's attack outcomes using conditional probability and the normal distribution. Students analyze how standard and critical attack modes affect total damage, and apply concepts such as the law of total probability, probability density functions, and Bayes' theorem. The scenario encourages understanding of how uncertainty and distributional assumptions can influence in-game mechanics and decision-making, blending mathematical reasoning with dynamic gameplay modeling.

This exercise explores probabilistic scenarios within a gaming context, where a character's attack power is normally distributed. You'll apply statistical techniques to calculate the likelihood of high-impact strikes, analyze expected outcomes across multiple actions, and assess the variability between successive attacks. Concepts include single-event probabilities, sums and differences of independent normal variables, and confidence interval calculations—all framed within a game-based narrative to make statistical reasoning more intuitive and engaging.