STAT 1000

uManitoba

Course Overview

Lessons & Practice

I. Welcome

1. Collecting Data & Sampling

44min

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

2. Experiments and Observational Studies

23min

2.1.1. Observational Studies4 min

2.1.2. Experimental Studies3 min

2.1.3. Example5 min

2.1.4. Practice

2.2.1. Types of Experimental Designs7 min

2.2.2. Principles of Experimental Design4 min

2.2.4. Practice

2.2.5. Practice

3. Displaying & Summarizing Quantitative Data

42min

3.1.1. Boxplots and Five Number Summary9 min

3.1.2. Practice4 min

3.1.3. Practice

3.2.1. Histograms4 min

3.2.2. Practice2 min

3.2.3. Practice2 min

3.2.4. Practice

3.3.1. Dot Plots5 min

3.3.2. Practice

3.4.1. Frequency Polygons2 min

3.4.2. Practice4 min

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

3.5.2. Practice3 min

3.6.1. Times Series Plots2 min

3.6.2. Practice2 min

4. Displaying & Summarizing Categorical Data

20min

4.1.1. Pie Chart3 min

4.1.2. Practice

4.2.1. Bar Chart3 min

4.2.2. Practice

4.3.1. Segmented Bar Chart (or Stacked Columns)3 min

4.3.2. Practice4 min

4.4.1. Contingency Table (Two-Way Table)4 min

4.4.2. Simpson’s Paradox3 min

4.4.3. Practice

5. Exploratory Data Analysis

49min

5.1.1. Measures of Central Tendency7 min

5.1.2. Mean and Median Example2 min

5.1.3. Practice

5.1.4. Practice2 min

5.1.5. Practice3 min

5.2.1. Skewness and Symmetry 6 min

5.2.2. Practice

5.3.1. Percentiles4 min

5.3.2. Example2 min

5.3.3. Practice

5.4.1. Range and Interquartile Range11 min

5.4.2. Variance and Standard Deviation6 min

5.4.3. Practice3 min

5.4.4. Practice3 min

5.4.5. Practice

6. Probability

1.9hr

6.1.1. Events & Sample Spaces6 min

6.1.2. Types of Probability6 min

6.1.3. Probability Language & Notation4 min

6.1.4. Example3 min

6.1.5. Independent vs. Mutually Exclusive Events4 min

6.1.6. Example2 min

6.1.7. Practice

6.2.1. Venn Diagrams3 min

6.2.2. Tree Diagrams4 min

6.2.3. Two-way Table5 min

6.3.1. Interpretation of Probability2 min

6.3.2. Complement Rule3 min

6.3.3. Practice1 min

6.3.4. The Addition Rule4 min

6.4.1. Probability of Independent Events4 min

6.4.2. Example3 min

6.4.3. Practice2 min

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

6.5.2. Conditional Probability: Tree Diagram5 min

6.5.3. Bayes’ Theorem4 min

6.5.4. Example4 min

6.5.5. Practice3 min

6.6.1. Example6 min

6.6.2. Example7 min

6.6.3. Example7 min

6.6.4. Practice4 min

6.6.5. Practice5 min

6.7.1. Summary of Key Definitions6 min

7. Counting Techniques

29min

7.1.1. Fundamental Counting Principle6 min

7.1.2. Permutations and Combinations6 min

7.1.3. Practice1 min

7.1.4. Practice54 sec

7.1.5. More Combination Rules3 min

7.1.6. Example4 min

7.1.7. Practice3 min

7.1.8. Practice

7.2.1. Counting and Probability3 min

7.2.3. Practice1 min

8. Discrete Random Variables

1.9hr

8.1.1. Discrete Random Variables8 min

8.1.2. Practice

8.1.3. Probability Distribution Function4 min

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

8.1.5. Example5 min

8.1.6. Example4 min

8.1.7. Practice6 min

8.1.8. Practice4 min

8.1.9. Practice

8.2.1. Transforming Data: Shifting & Scaling11 min

8.2.2. Practice2 min

8.2.3. Linear Transformation3 min

8.2.4. Example4 min

8.2.5. Practice2 min

8.3.1. Cumulative Distribution Function (CDF)3 min

8.3.2. Example6 min

8.3.3. Practice2 min

8.4.1. Combining Random Variables7 min

8.4.2. Example2 min

8.4.3. Practice2 min

8.4.4. Example3 min

8.4.5. Practice

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

8.4.7. Example3 min

8.4.8. Practice

8.4.9. Practice2 min

8.5.1. Conditional Probability & Joint Distribution7 min

8.5.2. Example5 min

8.5.3. Practice

8.5.4. Random Variables & Joint Distribution7 min

8.5.5. Example3 min

8.5.6. Practice

8.5.8. Practice

10. Continuous Probability Distributions

1.7hr

10.1.1. Continuous Probability Distribution Theory10 min

10.2.1. Uniform Distribution1 min

10.2.2. Practice3 min

10.3.1. Exponential Experiment3 min

10.3.2. Exponential Distribution7 min

10.3.3. Practice7 min

10.4.1. Normal Distribution11 min

10.4.2. Practice5 min

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

10.5.2. Standardizing a Normal Random Variable4 min

10.5.3. Example10 min

10.5.4. Practice6 min

10.5.5. Practice3 min

10.6.1. Normal Approximation to Binomial2 min

10.6.2. Practice5 min

10.6.3. Practice4 min

10.6.4. Practice4 min

10.7.1. Tchebysheff’s Theorem (Chebyshev's Theorem)3 min

10.7.2. Practice2 min

11. Sampling Distribution

59min

11.1.1. Sampling Variability & Sampling Distribution12 min

11.2.1. Central Limit Theorem 5 min

11.2.2. Sampling Distribution for a Mean2 min

11.2.3. Example9 min

11.2.4. Sampling Distribution for a Mean Question5 min

11.3.1. Sampling Distribution of Proportions5 min

11.3.2. Example3 min

11.3.3. Practice4 min

11.4.1. Drawing Samples From a Finite Population8 min

11.4.2. Example4 min

11.4.3. Practice3 min

12. Estimating with Confidence Intervals

48min

12.1.1. Introduction to Confidence Intervals14 min

12.2.1. Confidence Interval for a Mean13 min

12.2.2. Example4 min

12.2.3. Practice3 min

12.3.1. Confidence Interval for a Proportion2 min

12.3.2. Example5 min

12.3.3. Practice4 min

12.4.1. Margin of Error and Sample Size3 min

12.4.2. Practice

13. Hypothesis Testing with One Sample

1.9hr

13.1.1. Introduction to Hypothesis Testing 15 min

13.1.2. Hypothesis Testing Steps25 min

13.2.1. Hypothesis Test for a Mean3 min

13.2.2. Example16 min

13.2.3. Example8 min

13.2.4. Practice4 min

13.3.1. Hypothesis Test for a Proportion10 min

13.3.2. Example4 min

13.3.3. Practice5 min

13.3.4. Practice9 min

13.4.1. Type I and Type II Errors5 min

13.4.2. Type I and Type II Errors1 min

13.4.3. Practice

13.4.4. Practice

13.4.5. Power7 min

13.4.6. Practice

14. Inference for Two Population Means

1.6hr

14.1.1. Comparing Two Independent Means9 min

14.1.2. Hypothesis Test Steps: Comparing Two Independent Means11 min

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

14.2.2. Example (Unpooled)11 min

14.2.3. Practice (Unpooled)5 min

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

14.3.2. Example (Pooled)7 min

14.3.3. Practice (Pooled)7 min

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

14.4.2. Confidence Interval for Two Means Containing Zero7 min

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

14.5.1. Confidence Interval Unpooled t2 min

14.5.2. Example: Confidence Interval (Unpooled)5 min

14.5.3. Practice (Unpooled)

14.6.1. Confidence Interval Pooled t2 min

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

14.6.3. Practice (Pooled)

15. Match Pairs (Dependent Means)

37min

15.1.1. Match Pairs for Dependent Means12 min

15.2.1. Hypothesis Test for Matched Pairs11 min

15.2.2. Example7 min

15.2.3. Practice3 min

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

15.3.2. Practice

16. Inference for Two Population Proportions

49min

16.1.1. Hypothesis Testing for Two Independent Population Proportions9 min

16.1.2. Hypothesis Test Steps: Comparing Two Independent Proportions8 min

16.1.3. Example13 min

16.1.4. Practice (Pooled)6 min

16.2.1. Confidence Interval for Differences in Population Proportions3 min

16.2.2. Confidence Interval for Two Proportions1 min

16.2.3. Example4 min

16.2.4. Practice4 min

17. Scatterplots, Association, and Correlation

37min

17.1.1. Scatterplots5 min

17.1.2. Practice

17.2.1. Correlation5 min

17.2.2. Practice

17.3.1. Solving for Correlation2 min

17.3.2. Example6 min

17.3.3. Practice4 min

17.3.4. Example3 min

17.3.5. Practice

17.4.1. Coefficient of Determination (R Squared)7 min

17.4.2. Assessing Goodness of Fit6 min

17.4.3. Practice

18. Simple Linear Regression

45min

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

18.1.2. Example7 min

18.1.3. Practice (Version 1)3 min

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

18.1.5. Example5 min

18.1.6. Practice (Version 2)5 min

18.2.1. Predictions3 min

18.2.2. Residuals (Errors)5 min

18.2.3. Practice

18.2.4. Residual Plots2 min

18.2.5. Regression Diagnostics 5 min

18.2.6. Practice

18.2.7. Standard Deviation of the Residuals5 min

18.2.8. Practice

19. Inference for Linear Regression

2.2hr

19.1.1. Estimating the Coefficients of the Linear Regression Model9 min

19.1.2. Measures of Variation in Regression9 min

19.1.3. Practice

19.2.1. Standard Error and R Square Formulas7 min

19.2.2. Example5 min

19.2.3. Practice4 min

19.3.1. Confidence Interval for Linear Regression5 min

19.3.2. Example9 min

19.3.3. Practice3 min

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

19.3.5. Practice

19.4.1. Hypothesis Testing for Linear Regression14 min

19.4.2. Example17 min

19.4.3. Example13 min

19.4.4. Practice: Linear Regression Analysis6 min

19.5.1. Prediction Interval of Y7 min

19.5.2. Example12 min

19.5.3. Practice10 min

19.5.4. Practice

20. Multiple Regression

1.7hr

20.1.1. Assessing a Multiple Regression Model5 min

20.1.2. F-test for Multiple Regression5 min

20.1.3. Solving for the F-score9 min

20.1.4. Example2 min

20.1.5. Practice8 min

20.2.1. Hypothesis Testing for Multiple Regression (F-test)7 min

20.2.2. Example26 min

20.2.3. Example13 min

20.2.4. Practice13 min

20.2.5. Practice12 min

21. Chi-Square

48min

21.1.1. Types of Chi Square Tests8 min

21.1.2. Chi-Square Test for "Goodness of Fit"4 min

21.1.3. Example7 min

21.1.4. Pratice9 min

21.1.5. Chi-Square Test for Independence5 min

21.1.6. Example8 min

21.1.7. Practice4 min

21.1.8. More on Chi-Square Tests3 min

22. Inference about a Population Variance

41min

22.1.1. Inference for Population Variance & Chi-square Distribution 8 min

22.2.1. Confidence Interval for Population Variance5 min

22.2.2. Example6 min

22.2.3. Pratice3 min

22.2.4. Practice

22.3.1. Hypothesis Test for Population Variance8 min

22.3.2. Example8 min

22.3.3. Hypothesis Test for Population Variance

22.3.4. Practice4 min

23. Test of Equality of Two Variances

35min

23.1.1. Test of Equality of Two Variances7 min

23.2.1. F-Test for Equality of Two Variances11 min

23.2.2. Example6 min

23.2.3. F-Test for Equality of Two Variances

23.3.1. Levene’s Test for the Equality of Two Variances4 min

23.3.2. Example7 min

23.3.3. Practice

24. Analysis of Variance

38min

24.1.1. One-Way ANOVA8 min

24.1.2. One-Way ANOVA Table10 min

24.1.3. Example9 min

24.1.4. Practice

24.2.1. One-Way ANOVA Hypothesis Test6 min

24.2.2. Example4 min

24.2.3. Practice

Mock Exams

ME.1. Mock Exam21 Qns

ME.2. Mock Exam18 Qns

ME.3. Mock Exam27 Qns

ME.2 Mock Exam

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