HD STAT150 FULL SUMMARY NOTES

Description

Everything you need to ace Stat150! Includes diagrams and worked examples WEEK 1: INTRODUCTION TO STATISTICS 4 Objective and Scope of Statistics 4 Study Design 4 Types of Studies 4 Variables 4 Bias 4 Sample Size 4 Data Classification 4 WEEK 2: SUMMARISING AND DISPLAYING DATA 5 Graphs and Summaries for Categorical Data 5 Graphs and Summaries for Numerical Data 5 Histograms 5 Measures of Centre 5 Measures of Spread 5 Range 5 Interquartile range 5 Standard Deviation 5 WEEK 3: SUMMARISING AND GRAPHING NUMERICAL DATA 6 Mean or Median 6 Range, IQR or standard deviation 6 Box Plots 6 Fences 6 Whiskers 6 Outliers 6 Scatterplots 6 Population Distributions 7 WEEK 4: INTRODUCTION TO DISTRIBUTIONS 8 Introduction to Distributions 8 Random Variables 8 Discrete and Continuous Random Variables 8 Discrete and Continuous Distributions 8 Discrete Distributions: 8 The Binomial Distribution 8 Continuous Distributions: 8 The Normal Distribution 8 The Standard Normal Distribution 8 Areas Under a Normal Curve 8 Percentiles for a Normal Distribution 8 WEEK 5: PROPORTIONS 9 A Confidence Interval for Estimating p 9 WEEK 6: MEANS 10 The Central Limit Theorem 10 Standardising: z-scores 10 Confidence Intervals when the Standard Deviation is Known 10 1. Estimating the Mean: A Point Estimate 10 2. Estimating the Mean: An Interval Estimate 10 Confidence Interval when the Standard Deviation is Unknown 10 1. T-Critical Value 10 How do we Find t-Critical Values? 10 WEEK 7: HYPOTHESIS TESTS FOR A POPULATION MEAN 11 One Sample z-Test of a Population Mean 11 One Sample t-Test of a Population Mean 12 Standardising 12 WEEK 8: Comparing Population Means 13 Paired t-Test 13 95% Confidence Interval 13 Two Sample t-Test: 14 95% confidence interval 14 WEEK 9: SIMPLE LINEAR REGRESSION 15 The least squares regression line 15 Residuals 15 Interpretation 15 Assumptions of the linear model 15 Testing the slope of the least squares regression line 15 Hypothesis Test: Testing for a Linear Relationship 16 95% confidence interval for B1 16 WEEK 10: SIMPLE LINEAR REGRESSION-PART 2 17 Rules for Valid Predictions 17 Coefficient of Determination (R^2) 17 Correlation Coefficient (r) 17 WEEK 11: CATEGORICAL DATA ANALYSIS: PART 1 18 One sample z-Test for a Population Proportion 18 95% Confidence Interval for p 18 Chi Squared (𝜒2) Goodness-of-Fit Test 19 CATEGORICAL DATA ANALYSIS: PART 2 20 𝜒2 Test of Independence 20 Chi-Squared Test of Homogeneity 20 Displaying and Analysing Data 20