STAT 251

UBC

Course Overview

Lessons & Practice

I. Welcome

1. Overview and Descriptive Statistics

2.3hr

1.1.1. Introduction to Statistics4 min

1.1.2. Sample vs. Population7 min

1.1.3. Practice

1.1.4. Measurement Scales7 min

1.1.5. Practice

1.2.1. Statistical Sampling28 sec

1.2.2. Convenience Sampling1 min

1.2.3. Simple Random Sampling3 min

1.2.4. Systematic Sampling2 min

1.2.5. Stratified Sampling vs. Cluster Sampling6 min

1.2.6. Two-Stage Cluster Sampling2 min

1.2.7. Practice

1.2.8. Practice

1.2.9. Practice

1.3.1. Sampling Bias7 min

1.3.2. Recipe for a Good Sample5 min

1.3.3. Practice

1.3.4. Practice

1.4.1. Observational Studies4 min

1.4.2. Experimental Studies3 min

1.4.3. Example5 min

1.4.4. Practice

1.5.1. Types of Experimental Designs7 min

1.5.2. Principles of Experimental Design4 min

1.5.4. Practice

1.5.5. Practice

1.6.1. Histograms4 min

1.6.2. Practice2 min

1.6.3. Practice2 min

1.6.4. Practice

1.7.1. Dot Plots5 min

1.7.2. Practice

1.8.1. Frequency Polygons2 min

1.8.2. Practice4 min

1.9.1. Stemplots (Stem-and-Leaf Plots)2 min

1.9.2. Practice3 min

1.10.1. Measures of Central Tendency7 min

1.10.2. Mean and Median Example2 min

1.10.3. Practice

1.10.4. Practice2 min

1.10.5. Practice3 min

1.11.1. Skewness and Symmetry 6 min

1.11.2. Practice

1.12.1. Percentiles4 min

1.12.2. Example2 min

1.12.3. Practice

1.13.1. Range and Interquartile Range11 min

1.13.2. Variance and Standard Deviation6 min

1.13.3. Practice3 min

1.13.4. Practice3 min

1.13.5. Practice

2. Probability

2.4hr

2.1.1. Events & Sample Spaces6 min

2.1.2. Types of Probability6 min

2.1.3. Probability Language & Notation4 min

2.1.4. Example3 min

2.1.5. Independent vs. Mutually Exclusive Events4 min

2.1.6. Example2 min

2.1.7. Practice

2.2.1. Venn Diagrams3 min

2.2.2. Tree Diagrams4 min

2.2.3. Two-way Table5 min

2.3.1. Interpretation of Probability2 min

2.3.2. Complement Rule3 min

2.3.3. Practice1 min

2.3.4. The Addition Rule4 min

2.4.1. Probability of Independent Events4 min

2.4.2. Example3 min

2.4.3. Practice2 min

2.5.1. Probability of Dependent Events (Conditional Probability)7 min

2.5.2. Conditional Probability: Tree Diagram5 min

2.5.3. Bayes’ Theorem4 min

2.5.4. Example4 min

2.5.5. Practice3 min

2.6.1. Example6 min

2.6.2. Example7 min

2.6.3. Example7 min

2.6.4. Practice4 min

2.6.5. Practice5 min

2.7.1. Summary of Key Definitions6 min

2.8.1. Fundamental Counting Principle6 min

2.8.2. Permutations and Combinations6 min

2.8.3. Practice1 min

2.8.4. Practice54 sec

2.8.5. More Combination Rules3 min

2.8.6. Example4 min

2.8.7. Practice3 min

2.8.8. Practice

2.9.1. Counting and Probability3 min

2.9.3. Practice1 min

3. Discrete Random Variables and Probability Distributions

2.6hr

3.1.1. Discrete Random Variables8 min

3.1.2. Practice

3.1.3. Probability Distribution Function4 min

3.1.4. Expected Value, Variance, and Standard Deviation of Discrete Random Variables6 min

3.1.5. Example5 min

3.1.6. Example4 min

3.1.7. Practice6 min

3.1.8. Practice4 min

3.1.9. Practice

3.2.1. Transforming Data: Shifting & Scaling11 min

3.2.2. Practice2 min

3.2.3. Linear Transformation3 min

3.2.4. Example4 min

3.2.5. Practice2 min

3.3.1. Cumulative Distribution Function (CDF)3 min

3.3.2. Example6 min

3.3.3. Practice2 min

3.4.1. Bernoulli Trials4 min

3.4.2. Practice4 min

3.4.3. Binomial Experiment4 min

3.4.4. Binomial Distribution8 min

3.4.5. Example10 min

3.4.6. Example1 min

3.4.7. Practice6 min

3.4.8. Practice

3.5.1. Poisson Experiment5 min

3.5.2. Poisson Distribution1 min

3.5.3. Example3 min

3.5.4. Practice5 min

3.5.5. Practice5 min

3.6.1. Approximating the Binomial Distribution with Poisson2 min

3.6.2. Example6 min

3.6.3. Practice

3.7.1. Hypergeometric Experiment5 min

3.7.2. Hypergeometric Distribution9 min

3.7.3. Example4 min

3.7.4. Practice4 min

3.7.5. Practice Question

4. Continuous Probability Distributions

1.6hr

4.1.1. Continuous Probability Distribution Theory10 min

4.2.1. Uniform Distribution1 min

4.2.2. Practice3 min

4.3.1. Normal Distribution11 min

4.3.2. Practice5 min

4.4.1. Exponential Experiment3 min

4.4.2. Exponential Distribution7 min

4.4.3. Practice7 min

4.5.1. Standard Normal Distribution (Z-Scores)11 min

4.5.2. Standardizing a Normal Random Variable4 min

4.5.3. Example10 min

4.5.4. Practice6 min

4.5.5. Practice3 min

4.6.1. Normal Approximation to Binomial2 min

4.6.2. Practice5 min

4.6.3. Practice4 min

4.6.4. Practice4 min

5. Joint Probability Distributions and Random Variables

47min

5.1.1. Conditional Probability & Joint Distribution7 min

5.1.2. Example5 min

5.1.3. Practice

5.1.4. Random Variables & Joint Distribution7 min

5.1.5. Example3 min

5.1.6. Practice

5.1.8. Practice

5.2.1. Combining Random Variables7 min

5.2.2. Example2 min

5.2.3. Practice2 min

5.2.4. Example3 min

5.2.5. Practice

5.2.6. Functions of Two Independent Random Variables X and Y5 min

5.2.7. Example3 min

5.2.8. Practice

5.2.9. Practice2 min

6. Sampling Distribution

59min

6.1.1. Sampling Variability & Sampling Distribution12 min

6.2.1. Central Limit Theorem 5 min

6.2.2. Sampling Distribution for a Mean2 min

6.2.3. Example9 min

6.2.4. Sampling Distribution for a Mean Question5 min

6.3.1. Sampling Distribution of Proportions5 min

6.3.2. Example3 min

6.3.3. Practice4 min

6.4.1. Drawing Samples From a Finite Population8 min

6.4.2. Example4 min

6.4.3. Practice3 min

7. Estimating with Confidence Intervals

48min

7.1.1. Introduction to Confidence Intervals14 min

7.2.1. Confidence Interval for a Mean13 min

7.2.2. Example4 min

7.2.3. Practice3 min

7.3.1. Confidence Interval for a Proportion2 min

7.3.2. Example5 min

7.3.3. Practice4 min

7.4.1. Margin of Error and Sample Size3 min

7.4.2. Practice

7.5.1. Confidence Interval for Population Variance

7.5.2. Confidence Interval for Population Variance

8. Tests of Hypothesis Based on a Single Sample

1.9hr

8.1.1. Introduction to Hypothesis Testing 15 min

8.1.2. Hypothesis Testing Steps25 min

8.2.1. Hypothesis Test for a Mean3 min

8.2.2. Example16 min

8.2.3. Example8 min

8.2.4. Practice4 min

8.3.1. Hypothesis Test for a Proportion10 min

8.3.2. Example4 min

8.3.3. Practice5 min

8.3.4. Practice9 min

8.4.1. Type I and Type II Errors5 min

8.4.2. Type I and Type II Errors1 min

8.4.3. Practice

8.4.4. Practice

8.4.5. Power7 min

8.4.6. Practice

9. Inferences Based on Two Samples

3hr

9.1.1. Confidence Interval for Differences in Population Means (Pooled and Unpooled)6 min

9.1.2. Confidence Interval for Two Means Containing Zero7 min

9.1.3. Confidence Interval for Two Means (Independent Populations)9 min

9.2.1. Confidence Interval Unpooled t2 min

9.2.2. Example: Confidence Interval (Unpooled)5 min

9.2.3. Practice (Unpooled)

9.3.1. Confidence Interval Pooled t2 min

9.3.2. Example: Confidence Interval w/ Pooled T-test5 min

9.3.3. Practice (Pooled)

9.4.1. Comparing Two Independent Means9 min

9.4.2. Hypothesis Test Steps: Comparing Two Independent Means11 min

9.5.1. Unpooled t-test (Unequal Variances)4 min

9.5.2. Example (Unpooled)11 min

9.5.3. Practice (Unpooled)5 min

9.6.1. Pooled t-test (Equal Variances)3 min

9.6.2. Example (Pooled)7 min

9.6.3. Practice (Pooled)7 min

9.7.1. Match Pairs for Dependent Means12 min

9.8.1. Matched Pairs Confidence Interval for Differences in Two Dependent Population Means4 min

9.8.2. Practice

9.9.1. Hypothesis Test for Matched Pairs11 min

9.9.2. Example7 min

9.9.3. Practice3 min

9.10.1. Confidence Interval for Differences in Population Proportions3 min

9.10.2. Confidence Interval for Two Proportions1 min

9.10.3. Example4 min

9.10.4. Practice4 min

9.11.1. Hypothesis Testing for Two Independent Population Proportions9 min

9.11.2. Hypothesis Test Steps: Comparing Two Independent Proportions8 min

9.11.3. Example13 min

9.11.4. Practice (Pooled)6 min

9.12.1. Hypothesis Test for Population Variance

9.12.2. Hypothesis Test for Population Variance

9.12.3. Hypothesis Test for Population Variance

10. The Analysis of Variance

38min

10.1.1. One-Way ANOVA8 min

10.1.2. One-Way ANOVA Table10 min

10.1.3. Example9 min

10.1.4. Practice

10.2.1. One-Way ANOVA Hypothesis Test6 min

10.2.2. Example4 min

10.2.3. Practice

11. Multifactor Analysis of Variance

11min

11.1.1. Two-Way ANOVA with Replication Hypothesis Test5 min

11.1.2. Two-Way ANOVA with Replication Hypothesis Test6 min

12. Simple Linear Regression and Correlation

4hr

12.1.1. Scatterplots5 min

12.1.2. Practice

12.2.1. Correlation5 min

12.2.2. Practice

12.3.1. Solving for Correlation2 min

12.3.2. Example6 min

12.3.3. Practice4 min

12.3.4. Example3 min

12.3.5. Practice

12.4.1. Coefficient of Determination (R Squared)7 min

12.4.2. Assessing Goodness of Fit6 min

12.4.3. Practice

12.5.1. Solving for the Regression Line (r, Sy, Sx Method)5 min

12.5.2. Example7 min

12.5.3. Practice (Version 1)3 min

12.5.4. Solving for the Regression Line (Least Squares Method)2 min

12.5.5. Example5 min

12.5.6. Practice (Version 2)5 min

12.6.1. Predictions3 min

12.6.2. Residuals (Errors)5 min

12.6.3. Practice

12.6.4. Residual Plots2 min

12.6.5. Regression Diagnostics 5 min

12.6.6. Practice

12.6.7. Standard Deviation of the Residuals5 min

12.6.8. Practice

12.7.1. Estimating the Coefficients of the Linear Regression Model9 min

12.7.2. Measures of Variation in Regression9 min

12.7.3. Practice

12.8.1. Standard Error and R Square Formulas7 min

12.8.2. Example5 min

12.8.3. Practice4 min

12.9.1. Confidence Interval for Linear Regression5 min

12.9.2. Example9 min

12.9.3. Practice3 min

12.9.4. Slope: The Significance of "Zero" (or Lack Thereof)6 min

12.9.5. Practice

12.10.1. Hypothesis Testing for Linear Regression14 min

12.10.2. Example17 min

12.10.3. Example13 min

12.10.4. Practice: Linear Regression Analysis6 min

12.11.1. Prediction Interval of Y7 min

12.11.2. Example12 min

12.11.3. Practice10 min

12.11.4. Practice

Mock Exams

ME.1. Mock Exam21 Qns

ME.2. Mock Exam18 Qns

ME.3. Mock Exam27 Qns

ME.4. Midterm - Mock Assessment35 Qns

ME.5. Final Exam - Mock Assessment49 Qns

ME.2 Mock Exam

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