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AMS 7
UCSC
Course Overview
Lessons & Practice
I. Welcome
1 min
1. Collecting Data & Sampling
44min
1.1. Introduction to Statistics
0/5
1.1.1. Introduction to Statistics
4 min
1.1.2. Sample vs. Population
7 min
1.1.3. Practice
1.1.4. Measurement Scales
7 min
1.1.5. Practice
1.2. Statistical Sampling
0/9
1.2.1. Statistical Sampling
28 sec
1.2.2. Convenience Sampling
1 min
1.2.3. Simple Random Sampling
3 min
1.2.4. Systematic Sampling
2 min
1.2.5. Stratified Sampling vs. Cluster Sampling
6 min
1.2.6. Two-Stage Cluster Sampling
2 min
1.2.7. Practice
1.2.8. Practice
1.2.9. Practice
1.3. Good Sampling
0/4
1.3.1. Sampling Bias
7 min
1.3.2. Recipe for a Good Sample
5 min
1.3.3. Practice
1.3.4. Practice
2. Experiments and Observational Studies
23min
2.1. Experimental and Observational Studies
0/4
2.1.1. Observational Studies
4 min
2.1.2. Experimental Studies
3 min
2.1.3. Example
5 min
2.1.4. Practice
2.2. Types of Experimental Designs
0/5
2.2.1. Types of Experimental Designs
7 min
2.2.2. Principles of Experimental Design
4 min
2.2.3. Example
2.2.4. Practice
2.2.5. Practice
3. Displaying & Summarizing Quantitative Data
42min
3.1. Boxplots and Five-Number Summary
0/3
3.1.1. Boxplots and Five Number Summary
9 min
3.1.2. Practice
4 min
3.1.3. Practice
3.2. Histograms
0/4
3.2.1. Histograms
4 min
3.2.2. Practice
2 min
3.2.3. Practice
2 min
3.2.4. Practice
3.3. Dot Plots
0/2
3.3.1. Dot Plots
5 min
3.3.2. Practice
3.4. Frequency Polygons
0/2
3.4.1. Frequency Polygons
2 min
3.4.2. Practice
4 min
3.5. Stemplots
0/2
3.5.1. Stemplots (Stem-and-Leaf Plots)
2 min
3.5.2. Practice
3 min
3.6. Time Series Plots
0/2
3.6.1. Times Series Plots
2 min
3.6.2. Practice
2 min
4. Displaying & Summarizing Categorical Data
20min
4.1. Pie Charts
0/2
4.1.1. Pie Chart
3 min
4.1.2. Practice
4.2. Bar Charts
0/2
4.2.1. Bar Chart
3 min
4.2.2. Practice
4.3. Segmented Bar Charts
0/2
4.3.1. Segmented Bar Chart (or Stacked Columns)
3 min
4.3.2. Practice
4 min
4.4. Contingency Tables
0/3
4.4.1. Contingency Table (Two-Way Table)
4 min
4.4.2. Simpson’s Paradox
3 min
4.4.3. Practice
5. Exploratory Data Analysis
49min
5.1. Measures of Central Tendency
0/5
5.1.1. Measures of Central Tendency
7 min
5.1.2. Mean and Median Example
2 min
5.1.3. Practice
5.1.4. Practice
2 min
5.1.5. Practice
3 min
5.2. Skewness and Symmetry
0/2
5.2.1. Skewness and Symmetry
6 min
5.2.2. Practice
5.3. Percentiles
0/3
5.3.1. Percentiles
4 min
5.3.2. Example
2 min
5.3.3. Practice
5.4. Measure of Variability
0/5
5.4.1. Range and Interquartile Range
11 min
5.4.2. Variance and Standard Deviation
6 min
5.4.3. Practice
3 min
5.4.4. Practice
3 min
5.4.5. Practice
6. Probability
1.9hr
6.1. Introduction to Probability
0/7
6.1.1. Events & Sample Spaces
6 min
6.1.2. Types of Probability
6 min
6.1.3. Probability Language & Notation
4 min
6.1.4. Example
3 min
6.1.5. Independent vs. Mutually Exclusive Events
4 min
6.1.6. Example
2 min
6.1.7. Practice
6.2. Tools for Probability
0/3
6.2.1. Venn Diagrams
3 min
6.2.2. Tree Diagrams
4 min
6.2.3. Two-way Table
5 min
6.3. Basic Rules of Probability
0/4
6.3.1. Interpretation of Probability
2 min
6.3.2. Complement Rule
3 min
6.3.3. Practice
1 min
6.3.4. The Addition Rule
4 min
6.4. Probability of Independent Events
0/3
6.4.1. Probability of Independent Events
4 min
6.4.2. Example
3 min
6.4.3. Practice
2 min
6.5. Probability of Dependent Events (Conditional Probability)
0/5
6.5.1. Probability of Dependent Events (Conditional Probability)
7 min
6.5.2. Conditional Probability: Tree Diagram
5 min
6.5.3. Bayes’ Theorem
4 min
6.5.4. Example
4 min
6.5.5. Practice
3 min
6.6. Probability Problems
0/5
6.6.1. Example
6 min
6.6.2. Example
7 min
6.6.3. Example
7 min
6.6.4. Practice
4 min
6.6.5. Practice
5 min
6.7. Summary of Key Definitions
0/1
6.7.1. Summary of Key Definitions
6 min
7. Counting Techniques
29min
7.1. Counting Techniques
0/8
7.1.1. Fundamental Counting Principle
6 min
7.1.2. Permutations and Combinations
6 min
7.1.3. Practice
1 min
7.1.4. Practice
54 sec
7.1.5. More Combination Rules
3 min
7.1.6. Example
4 min
7.1.7. Practice
3 min
7.1.8. Practice
7.2. Counting and Probability
0/3
7.2.1. Counting and Probability
3 min
7.2.2. Example
7.2.3. Practice
1 min
8. Discrete Random Variables
1.9hr
8.1. Randomness and Probability
0/9
8.1.1. Discrete Random Variables
8 min
8.1.2. Practice
8.1.3. Probability Distribution Function
4 min
8.1.4. Expected Value, Variance, and Standard Deviation of Discrete Random Variables
6 min
8.1.5. Example
5 min
8.1.6. Example
4 min
8.1.7. Practice
6 min
8.1.8. Practice
4 min
8.1.9. Practice
8.2. Linear Transformation of Data
0/5
8.2.1. Transforming Data: Shifting & Scaling
11 min
8.2.2. Practice
2 min
8.2.3. Linear Transformation
3 min
8.2.4. Example
4 min
8.2.5. Practice
2 min
8.3. Cumulative Distribution Function
0/3
8.3.1. Cumulative Distribution Function (CDF)
3 min
8.3.2. Example
6 min
8.3.3. Practice
2 min
8.4. Combining Random Variables
0/9
8.4.1. Combining Random Variables
7 min
8.4.2. Example
2 min
8.4.3. Practice
2 min
8.4.4. Example
3 min
8.4.5. Practice
8.4.6. Functions of Two Independent Random Variables X and Y
5 min
8.4.7. Example
3 min
8.4.8. Practice
8.4.9. Practice
2 min
8.5. Joint Distribution
0/8
8.5.1. Conditional Probability & Joint Distribution
7 min
8.5.2. Example
5 min
8.5.3. Practice
8.5.4. Random Variables & Joint Distribution
7 min
8.5.5. Example
3 min
8.5.6. Practice
8.5.7. Example
8.5.8. Practice
9. Discrete Probability Distributions
1.4hr
9.1. Binomial Distribution
0/8
9.1.1. Bernoulli Trials
4 min
9.1.2. Practice
4 min
9.1.3. Binomial Experiment
4 min
9.1.4. Binomial Distribution
8 min
9.1.5. Example
10 min
9.1.6. Example
1 min
9.1.7. Practice
6 min
9.1.8. Practice
9.2. Poisson Distribution
0/5
9.2.1. Poisson Experiment
5 min
9.2.2. Poisson Distribution
1 min
9.2.3. Example
3 min
9.2.4. Practice
5 min
9.2.5. Practice
5 min
9.3. Approximating the Binomial Distribution with Poisson
0/3
9.3.1. Approximating the Binomial Distribution with Poisson
2 min
9.3.2. Example
6 min
9.3.3. Practice
9.4. Hypergeometric Probability
0/5
9.4.1. Hypergeometric Experiment
5 min
9.4.2. Hypergeometric Distribution
9 min
9.4.3. Example
4 min
9.4.4. Practice
4 min
9.4.5. Practice Question
10. Continuous Probability Distributions
1.7hr
10.1. Continuous Probability Distribution
0/1
10.1.1. Continuous Probability Distribution Theory
10 min
10.2. Uniform Distribution
0/2
10.2.1. Uniform Distribution
1 min
10.2.2. Practice
3 min
10.3. Exponential Distribution
0/3
10.3.1. Exponential Experiment
3 min
10.3.2. Exponential Distribution
7 min
10.3.3. Practice
7 min
10.4. Normal Distribution
0/2
10.4.1. Normal Distribution
11 min
10.4.2. Practice
5 min
10.5. Standardizing
0/5
10.5.1. Standard Normal Distribution (Z-Scores)
11 min
10.5.2. Standardizing a Normal Random Variable
4 min
10.5.3. Example
10 min
10.5.4. Practice
6 min
10.5.5. Practice
3 min
10.6. Normal Approximation to Binomial
0/4
10.6.1. Normal Approximation to Binomial
2 min
10.6.2. Practice
5 min
10.6.3. Practice
4 min
10.6.4. Practice
4 min
10.7. Tchebysheff’s Theorem (Chebyshev's Theorem)
0/2
10.7.1. Tchebysheff’s Theorem (Chebyshev's Theorem)
3 min
10.7.2. Practice
2 min
11. Sampling Distribution
59min
11.1. Intro to Sampling Distribution
0/1
11.1.1. Sampling Variability & Sampling Distribution
12 min
11.2. Sampling Distribution for a Mean
0/4
11.2.1. Central Limit Theorem
5 min
11.2.2. Sampling Distribution for a Mean
2 min
11.2.3. Example
9 min
11.2.4. Sampling Distribution for a Mean Question
5 min
11.3. Sampling Distribution for a Proportion
0/3
11.3.1. Sampling Distribution of Proportions
5 min
11.3.2. Example
3 min
11.3.3. Practice
4 min
11.4. Finite Population Sampling
0/3
11.4.1. Drawing Samples From a Finite Population
8 min
11.4.2. Example
4 min
11.4.3. Practice
3 min
12. Estimating with Confidence Intervals
48min
12.1. Introduction to Confidence Intervals
0/1
12.1.1. Introduction to Confidence Intervals
14 min
12.2. Confidence Interval for a Mean
0/3
12.2.1. Confidence Interval for a Mean
13 min
12.2.2. Example
4 min
12.2.3. Practice
3 min
12.3. Confidence Interval for a Proportion
0/3
12.3.1. Confidence Interval for a Proportion
2 min
12.3.2. Example
5 min
12.3.3. Practice
4 min
12.4. Margin of Error and Sample Size
0/2
12.4.1. Margin of Error and Sample Size
3 min
12.4.2. Practice
13. Hypothesis Testing with One Sample
1.9hr
13.1. Introduction to Hypothesis Testing
0/2
13.1.1. Introduction to Hypothesis Testing
15 min
13.1.2. Hypothesis Testing Steps
25 min
13.2. Hypothesis Test for a Mean
0/4
13.2.1. Hypothesis Test for a Mean
3 min
13.2.2. Example
16 min
13.2.3. Example
8 min
13.2.4. Practice
4 min
13.3. Hypothesis Test for a Proportion
0/4
13.3.1. Hypothesis Test for a Proportion
10 min
13.3.2. Example
4 min
13.3.3. Practice
5 min
13.3.4. Practice
9 min
13.4. Type I and Type II Errors
0/6
13.4.1. Type I and Type II Errors
5 min
13.4.2. Type I and Type II Errors
1 min
13.4.3. Practice
13.4.4. Practice
13.4.5. Power
7 min
13.4.6. Practice
14. Inference for Two Population Means
1.6hr
14.1. Hypothesis Testing for Two Independent Means
0/2
14.1.1. Comparing Two Independent Means
9 min
14.1.2. Hypothesis Test Steps: Comparing Two Independent Means
11 min
14.2. Unpooled t-test
0/3
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. Pooled t-test
0/3
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. Confidence Interval for Two Independent Means
0/3
14.4.1. Confidence Interval for Differences in Population Means (Pooled and Unpooled)
6 min
14.4.2. Confidence Interval for Two Means Containing Zero
7 min
14.4.3. Confidence Interval for Two Means (Independent Populations)
9 min
14.5. Confidence Interval Unpooled t
0/3
14.5.1. Confidence Interval Unpooled t
2 min
14.5.2. Example: Confidence Interval (Unpooled)
5 min
14.5.3. Practice (Unpooled)
14.6. Confidence Interval Pooled t
0/3
14.6.1. Confidence Interval Pooled t
2 min
14.6.2. Example: Confidence Interval w/ Pooled T-test
5 min
14.6.3. Practice (Pooled)
15. Match Pairs (Dependent Means)
37min
15.1. Matched Pairs
0/1
15.1.1. Match Pairs for Dependent Means
12 min
15.2. Hypothesis Testing for Matched Pairs
0/3
15.2.1. Hypothesis Test for Matched Pairs
11 min
15.2.2. Example
7 min
15.2.3. Practice
3 min
15.3. Confidence Intervals for Matched Pairs
0/2
15.3.1. Matched Pairs Confidence Interval for Differences in Two Dependent Population Means
4 min
15.3.2. Practice
16. Inference for Two Population Proportions
49min
16.1. Hypothesis Testing for Two Proportions
0/4
16.1.1. Hypothesis Testing for Two Independent Population Proportions
9 min
16.1.2. Hypothesis Test Steps: Comparing Two Independent Proportions
8 min
16.1.3. Example
13 min
16.1.4. Practice (Pooled)
6 min
16.2. Confidence Interval for Two Proportions
0/4
16.2.1. Confidence Interval for Differences in Population Proportions
3 min
16.2.2. Confidence Interval for Two Proportions
1 min
16.2.3. Example
4 min
16.2.4. Practice
4 min
17. Scatterplots, Association, and Correlation
37min
17.1. Scatterplots
0/2
17.1.1. Scatterplots
5 min
17.1.2. Practice
17.2. Correlation
0/2
17.2.1. Correlation
5 min
17.2.2. Practice
17.3. Solving for Correlation
0/5
17.3.1. Solving for Correlation
2 min
17.3.2. Example
6 min
17.3.3. Practice
4 min
17.3.4. Example
3 min
17.3.5. Practice
17.4. Coefficient of Determination
0/3
17.4.1. Coefficient of Determination (R Squared)
7 min
17.4.2. Assessing Goodness of Fit
6 min
17.4.3. Practice
18. Simple Linear Regression
45min
18.1. Solving for the Regression Line
0/6
18.1.1. Solving for the Regression Line (r, Sy, Sx Method)
5 min
18.1.2. Example
7 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. Example
5 min
18.1.6. Practice (Version 2)
5 min
18.2. Predictions and Residual Plots
0/8
18.2.1. Predictions
3 min
18.2.2. Residuals (Errors)
5 min
18.2.3. Practice
18.2.4. Residual Plots
2 min
18.2.5. Regression Diagnostics
5 min
18.2.6. Practice
18.2.7. Standard Deviation of the Residuals
5 min
18.2.8. Practice
19. Inference for Linear Regression
2.2hr
19.1. Simple Linear Regression Analysis
0/3
19.1.1. Estimating the Coefficients of the Linear Regression Model
9 min
19.1.2. Measures of Variation in Regression
9 min
19.1.3. Practice
19.2. Standard Error and R-Square
0/3
19.2.1. Standard Error and R Square Formulas
7 min
19.2.2. Example
5 min
19.2.3. Practice
4 min
19.3. Confidence Intervals for Regression
0/5
19.3.1. Confidence Interval for Linear Regression
5 min
19.3.2. Example
9 min
19.3.3. Practice
3 min
19.3.4. Slope: The Significance of "Zero" (or Lack Thereof)
6 min
19.3.5. Practice
19.4. Hypothesis Testing for Linear Regression
0/4
19.4.1. Hypothesis Testing for Linear Regression
14 min
19.4.2. Example
17 min
19.4.3. Example
13 min
19.4.4. Practice: Linear Regression Analysis
6 min
19.5. Prediction Intervals for Y
0/4
19.5.1. Prediction Interval of Y
7 min
19.5.2. Example
12 min
19.5.3. Practice
10 min
19.5.4. Practice
20. Multiple Regression
1.7hr
20.1. Multiple Regression Model
0/5
20.1.1. Assessing a Multiple Regression Model
5 min
20.1.2. F-test for Multiple Regression
5 min
20.1.3. Solving for the F-score
9 min
20.1.4. Example
2 min
20.1.5. Practice
8 min
20.2. Hypothesis Testing for Multiple Regression
0/5
20.2.1. Hypothesis Testing for Multiple Regression (F-test)
7 min
20.2.2. Example
26 min
20.2.3. Example
13 min
20.2.4. Practice
13 min
20.2.5. Practice
12 min
21. Chi-Square
48min
21.1. Chi-Square
0/8
21.1.1. Types of Chi Square Tests
8 min
21.1.2. Chi-Square Test for "Goodness of Fit"
4 min
21.1.3. Example
7 min
21.1.4. Pratice
9 min
21.1.5. Chi-Square Test for Independence
5 min
21.1.6. Example
8 min
21.1.7. Practice
4 min
21.1.8. More on Chi-Square Tests
3 min
22. Inference about a Population Variance
41min
22.1. Inference for Population Variance & Chi-square Distribution
0/1
22.1.1. Inference for Population Variance & Chi-square Distribution
8 min
22.2. Confidence Interval for Population Variance
0/4
22.2.1. Confidence Interval for Population Variance
5 min
22.2.2. Example
6 min
22.2.3. Pratice
3 min
22.2.4. Practice
22.3. Hypothesis Test for Population Variance
0/4
22.3.1. Hypothesis Test for Population Variance
8 min
22.3.2. Example
8 min
22.3.3. Hypothesis Test for Population Variance
22.3.4. Practice
4 min
23. Test of Equality of Two Variances
35min
23.1. Test of Equality of Two Variances
0/1
23.1.1. Test of Equality of Two Variances
7 min
23.2. F-Test for Equality of Two Variances
0/3
23.2.1. F-Test for Equality of Two Variances
11 min
23.2.2. Example
6 min
23.2.3. F-Test for Equality of Two Variances
23.3. Levene’s Test for the Equality of Two Variances
0/3
23.3.1. Levene’s Test for the Equality of Two Variances
4 min
23.3.2. Example
7 min
23.3.3. Practice
24. Analysis of Variance
38min
24.1. One-Way ANOVA
0/4
24.1.1. One-Way ANOVA
8 min
24.1.2. One-Way ANOVA Table
10 min
24.1.3. Example
9 min
24.1.4. Practice
24.2. Hypothesis Testing for One-Way ANOVA
0/3
24.2.1. One-Way ANOVA Hypothesis Test
6 min
24.2.2. Example
4 min
24.2.3. Practice
Mock Exams
ME.1. Mock Exam
21 Qns
ME.2. Mock Exam
18 Qns
ME.3. Mock Exam
27 Qns
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