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Normal Distrbution - Vehicle Repairs Example
Vehcile repair time
Difference In Proportions Mobiile Phone Ownership
Difference In Proportions Mobiile Phone Ownership
Coal Fired Power Station
Coal Fired Power Station
Estimating the Difference in Proportions Between Two Communities
Estimating the Difference in Proportions Between Two Communities
Age and Voting Preference: A Hypothesis Test
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
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.
Source Coding - Worked Example
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 in Information Theory
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
Data compression is driven by the need to enhance the efficiency of digital information processing.
Kraft Inequality
Theory on the Kraft Inequality
Mutual Information
Theory of Mutual Information in Information Theory
Analyzing Horse Weights with Normal Distribution Models
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.
Conditional Probability and Damage Modeling in Role-Playing Games
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.
Strategic Combat Analysis Using the Normal Distribution
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.
Fresha Tea Company - Normal Distribution Worked Example
Fresha Tea Company - Normal Distribution Worked Example
Normal Distribution - Product Sales Worked Example
Product Sales of a Telecommunications Company
Expected Values in the Chi Square Test
Computing Expected Values for a contingency Table
Paired t-Test: A Step-by-Step Guide
A paired t-test is a statistical method used to determine whether there is a significant difference between two sets of related observations. It’s especially useful when the same subjects are measured under two different conditions
The Chi-Squared Test
Tutorial on the Chi Square Test
FriedMan Text
Friedman Rank Sum Test
Implementation of the Friedman Test using the Warpbreaks data set
Poisson Approximation to the Binomial Distribution
This exercise demonstrates how the Poisson distribution can approximate a binomial distribution when trials are large and success probabilities are small. It includes step-by-step examples, comparisons, and practical use cases for real-world data
The Uniform Probability Distribution
Tutorial on the Uniform Probability Distribution
The Binomial Text with R
Tutorial on the Binomial Text with R
Gambler's Ruin
This simulation explores the classic Gambler’s Ruin problem using R. It models a series of biased coin tosses between a gambler and a banker, tracks the gambler’s fortune over time, and analyzes the duration and outcomes of multiple trials.
Benford's Law
Tutorial on Benford's Law
The Hypergeometric Probability Distribution
Tutorial on the Hypergeometric Probability Distribution
The Geometric Probabaility Distribution
Tutorial Sheet for the Geometric Probability Distribution
The Exponential Probability Distribution
Tutorial on the exponential probability distribution
The Weibull Probability Distribution
Tutorial on the Weibull Probability Distribution - The Weibull distribution is widely used for life data analysis. Among its variations, the two-parameter Weibull distribution is the most common, though the three-parameter and one-parameter versions are also utilized for more detailed analysis.
The Lognormal Probability Distribution
Short tutorial on the Lognormal Probability Distribution
Introduction to Statistical Process Control
Introduction to Statistical Process Control
Barley Yield Example - Paired t-test
In the built-in data set named **`immer`**, the barley yield in years 1931 and 1932 for the same fields is recorded.
Fertilizer treatments were applied in the interim. The study aimed to determine whether the treatment was effective.
Bartlett's test for Homogeneity of Variances
Bartlett's test for Homogeneity of Variances
Anderson Darling Test for Normality
The Anderson-Darling test evaluates whether a sample follows a specific distribution, typically normal. It gives more weight to tail behaviour than other tests, making it sensitive to subtle deviations.
Mitigating Non-Normality with Logarithmic Transformation
This tutorial explains how log transformation can correct non-normal data, helping restore normality for valid statistical analysis—especially useful with skewed data or small sample sizes.
Kolmogorov-Smirnov Test
The Kolmogorov-Smirnov (K-S) test is a non-parametric method used to compare a sample's distribution to a fully specified continuous theoretical distribution.