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Sandahl Nelson

Sandahl Nelson

Hypothesis Testing

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Table of Contents

Section 1: Describing Data: Graphically & Numerically
Constructing & Interpreting Graphs

37m 14s

Intro
0:00
Objectives
0:08
Categorical Data
0:26
Pie Charts
0:27
Bar Graphs
1:20
(More) Bar Graphs
2:25
Comparative
2:26
Relative Frequency
3:30
Numerical Data: Discrete
4:35
Dot Plots
4:36
Stem and Leaf Plots
6:08
Example: Stem Plot
7:55
Example: Stem Plot
7:56
Numerical Data: Continuous
9:03
Numerical Data (Continuous)
9:04
Example I: Histogram
10:57
Numerical Data: Cumulative Frequency Plots
16:49
Frequency Polygon
16:50
Ogive Plot
18:00
Describe the Distribution
19:42
SOCS: Shape, Outlier, Center, Spread
19:43
Shape
20:28
Unimodal, Bimodal, or Multimodal
20:29
Symmetric Distribution
21:48
Positively Skewed Distribution
21:30
Negatively Skewed Distribution
21:46
Example II: Describe the Distribution
22:06
Stem Plots to Compare Two Groups of Data
23:06
Stem Plots to Compare Two Groups of Data
23:06
Example III: Compare the Distribution
23:47
Example IV: Describe the Distribution of Quiz Scores
27:45
Example V: Stem Plot
29:26
Example VI: Bar Graph & Relative Frequency
30:53
Summarizing Distributions of Univariate Data

1h 7m 37s

Intro
0:00
Objectives
0:10
Measuring Center
0:42
Median
0:43
Mean
0:56
Example: Find the Median and Mean
1:59
Measuring Position
6:59
Percentiles
7:10
Quartiles
7:39
Example: Find the Quartiles
8:58
Measuring Spread
11:13
Range
11:14
IQR
11:33
Variance
11:55
Example: Measuring Spread
13:21
Example: Find the Measures of Spread
22:09
Outliers
27:23
Outliers
27:24
Example: Outliers
29:05
Boxplots
31:44
5-number Summary
31:45
Example I: Boxplot
33:55
Describe the Distribution
44:20
SOCS: Shape, Outlier, Center, Spread
44:21
Choosing Your Measure of Center & Spread
45:16
Example II: Describe the Distribution
46:08
The Effect of Changing Units on Summary Measures
48:26
Linear Transformations
48:27
Example: Distribution of Ages
50:42
Example III: Modified Boxplot & Describe the Distribution
53:26
Example IV: Describe the Distribution
1:02:37
Section 2: Correlation & Regression
Correlation & Regression

50m 16s

Intro
0:00
Objectives
0:07
Scatterplots
0:30
Scatterplots
0:31
Interpreting Scatterplots
2:20
Direction
2:34
Form
2:50
Strength
3:29
Example: Describe the Direction, Form, and Strength of the Scatterplot
4:00
Correlation Coefficient ( r )
5:22
Correlation Coefficient ( r )
5:23
Example: Correlation Coefficient ( r )
7:52
Approximate the Correlation Coefficient
7:53
Interpret the Correlation Coefficient
8:48
Least Squares Regression Line (LSRL)
9:23
Least Squares Regression Line (LSRL)
9:24
Interpreting the LSRL
10:45
y-intercept, Slope, Mean, and SD
10:46
Example: Interpreting the LSRL
14:48
Step 1: Determine the Least-squares Regression Line
14:49
Step 2: Interpret the Slope and y-intercept of the Regression Line
18:28
Step 3: Interpret the Correlation
20:56
Coefficient of Determination
23:50
R² = (r)²
23:51
Residuals
26:04
Residual = Observed y - Predicted y
26:05
Residual Plot
27:04
Example: Calculate the Residual
28:33
Example: Draw the Residual Plot
31:18
Example I: Explanatory Variable & Response Variable
37:47
Example II: Find the Least-squares Regression Line
39:08
Example III: Calculate the Residual
44:10
Example IV: Predicted Value
47:50
Example V: Residual Value
49:28
Regression, Part II

23m 26s

Intro
0:00
Objectives
0:10
Outliers and Influential Points
0:20
An OUTLIER
0:21
Influential Observations
1:05
Transformations to Achieve Linearity
2:39
Transformations to Achieve Linearity: When We Need It
2:40
Transformations to Achieve Linearity: How We Use It
4:41
Example I: Expected Number of Sales
7:11
Confounding
11:13
Confounding
11:14
Correlation Does NOT Prove Causation
11:55
Correlation Does NOT Prove Causation
11:56
Lurking Variables
13:06
Lurking Variables & Common Response
13:07
Confounding
14:25
Confounding
14:26
Example: Promotion to Increase Movie Sales
15:11
Example II: Causation, Confounding, or Common Response
16:26
Example III: Correlation
18:25
Example IV: Confounding & Common Response
19:50
Section 3: Surveys & Experiments
Planning & Conducting Surveys

29m 35s

Intro
0:00
Objectives
0:09
Census vs. Survey, Parameter vs. Statistics
0:28
Census vs. Survey, Parameter vs. Statistics
0:29
Characteristics of a Well-Designed and Well-Conducted Survey
2:15
Representative Sample
2:16
Random Sample
3:38
Does Not Introduce Bias
4:02
Bias
4:16
What Is It?
4:17
How Might It Occur?
5:26
Example I: Identify the Type of Bias
7:03
Random Sampling
10:25
Simple Random Sample (SRS)
10:26
Example II: Random Sampling
13:26
Random Sampling, Cont.
16:44
Stratified Random Sampling
16:55
Cluster Sample
18:06
Systematic Random Sample
19:16
Example III: Random Sampling
20:52
Non-Random Sampling
22:28
Convenience Sample
22:29
Voluntary Response Sample
22:54
Example IV: Sampling Design
25:01
Specify The Population
25:02
Describe The Sampling Design. Will You Use a Stratified Sample?
26:46
Planning & Conducting Experiments

41m 31s

Intro
0:00
Objectives
0:09
Experiments vs. Observational Studies
0:44
Observational Study
0:45
Experiment
1:28
Example I: Experimental or Observational?
2:09
Example II: Experimental or Observational?
2:57
Placebo Effect
3:51
Placebo Effect
3:52
Characteristics of a Well-designed and Well-conducted Experiment
4:42
Control
4:43
Replicate
5:32
Randomize
6:32
Example III: Control Groups
7:33
Completely Randomized Design
9:01
Completely Randomized Design
9:02
Outline/Map of Completely Randomized Design
9:55
Outline/Map of Completely Randomized Design
9:56
Example IV: Completely Randomized Design
11:35
Block Randomization
14:23
Block Randomization
14:24
Randomized Block Design
15:29
Randomized Block Design
15:30
Example V: Randomized Block Design
18:06
Matched Pairs Design
21:08
Matched Pairs Design
21:09
Example V: Types of Experiments
22:42
Example VI: Types of Experiments
24:17
Example VII: Types of Experiments
26:24
Experimental Set Up
28:28
Treatment
28:29
Experimental Units
29:13
Response
29:32
Double-blind Experiment
31:06
Double-blind Experiment
31:07
Example VIII: Double-blind Experiment
32:37
Example IX: Design a Study to Test Hypothesis
37:04
Generalizability of Results
40:39
Statistically Significant Data
40:40
Section 4: Probability & Expected Value
Probability Overview

1h 22m 17s

Intro
0:00
Objectives
0:21
Interpreting Probability
0:46
Probability of a Random Outcome or the Long Term Relative Frequency
0:47
Law of Large Numbers
1:42
Expected Value
1:43
Example I: Probability in Poker
2:21
Probability Model
4:31
Sample Space (S)
4:32
Event
5:15
Probabilities
6:03
Example II: Basketball Free Throws
6:37
Part 1: Sample Space
6:46
Part 2: Event
8:08
Part 3: Probability
8:48
Disjoin Events (aka Mutually Exclusive)
11:00
Disjoin Events (aka Mutually Exclusive)
11:01
Example III: Advertising Contracts
12:23
Part A: Venn Diagram
12:24
Probability of Disjoin Events
14:03
Probability of Disjoin Events
14:04
Example IV: Probability of Disjoin Events
15:58
Independence vs. Dependence
18:11
Independence vs. Dependence
18:12
Example V: Independence vs. Dependence
20:26
Example VI: Independence vs. Dependence
22:23
Probability Rules
23:13
Probability Rules
23:14
Probability Notation
23:31
P (A or B)
23:32
P (A and B)
23:58
P ( A given B happened)
24:24
P ( not A)
24:44
Example VII: Probability Notation
25:17
Probability Rule Notation
26:49
A or B
26:50
A and B
27:40
Example VIII: Determine if These Two Events are Independent
29:05
Example IX: Conditional Probability of Wining
31:39
Example X: Conditional Probability of Students
36:46
Part A: Probability
36:47
Part B: Conditional Probability
38:18
Part C: Conditional Probability
39:59
Example XI: Conditional Probability of Children
42:53
Part A: All Boys
42:54
Part B: All Girls
44:44
Part C: Exactly Two Boys or Exactly Two Girls
45:50
Part D: At Least One Child of Each Sex
50:18
Overview
52:52
Complement
52:53
Mutually Exclusive
53:30
Intersection
53:49
Union
54:44
Independent
55:34
Bayes Rule
56:02
Bayes Rule
56:03
Example XI: Probability & Bayes Rule
59:43
Example XII: Probability & Bayes Rule
1:07:49
Simulations
1:05:46
Simulations
1:05:47
Example XIII: Simulations
1:07:10
Intro to Probability for Discrete Random Variables

31m 37s

Intro
0:00
Objectives
0:09
Discrete vs. Continuous Random Variables
0:29
Discrete Random Variables
0:30
Continuous Random Variables
1:12
Probability Distribution
3:36
Probability Distribution for a Discrete Random Variables
3:37
Probability Rules
4:20
Example I: Find the Probability
4:51
Example II: Construct a Probability Distribution
6:15
Mean
9:35
Expected Value
9:36
Example: Expected Number of Customers
10:08
Variance
13:19
Variance
13:20
Example: Variance
14:34
Example III: Probability Analysis
18:01
Example IV: Expected Profit
25:25
Discrete Random Variables

39m 6s

Intro
0:00
Objectives
0:08
Binomial Distribution
0:14
BINP
0:15
B
0:34
I
0:49
N
1:00
P
1:20
Example I: Binomial Distribution
1:43
Question 1: Is a Binomial Distribution a Reasonable Probability Model for the Random Variable X?
1:44
Question 2: Is a Binomial Distribution a Reasonable Probability Model for the Random Variable X?
3:43
Binomial Probability
5:11
Binompdf (n, p, x)
5:12
Example II: Determine the Probability
10:37
Part A: Determine the Probability that Exactly One of the Toasters is Defective
10:38
Part B: Determine the Probability that At Most Two of the Toasters are Defective
16:40
Part C: Determine the Probability that More Than Three of the Toasters are Defective
21:42
Geometric Distribution
24:11
Geometric Distribution
24:12
Example III: Geometric Distribution & Probability
25:14
Part A: Geometric Distribution
25:15
Geometric Probability
26:55
Geometpdf (p, x)
26:56
Example III: Geometric Distribution & Probability
27:50
Part B: Geometric Probability of Exactly Four Patients
27:51
Part C: Geometric Probability of At Most Five Patients
31:19
Mean and SDs
33:47
Binomial
33:48
Geometric
34:28
Example IV: Defective Units
34:53
Example V: Number of Patients
35:58
Combining Independent Random Variables

18m 56s

Intro
0:00
Objectives
0:09
Mean and Standard Deviation of Two Random Variables
0:26
Mean and Standard Deviation of Two Random Variables
0:27
Example I: Average and Standard Deviation
1:58
Example II: Average and Standard Deviation
4:37
Transforming Random Variables: “Linear Transformations”
6:10
Transforming Random Variables: “Linear Transformations”
6:11
Example III: Mean and Standard Deviation
7:02
Example IV: Mean and Standard Deviation
10:23
Example V: Mean and Standard Deviation
14:14
Part 1: Mean & SD
14:15
Part 2: Mean & SD
16:30
Normal Random Variables

59m 34s

Intro
0:00
Objectives
0:08
The Empirical Rule
0:28
68%
0:29
95%
1:43
99.70%
2:00
The Empirical Rule, Cont.
2:31
The Empirical Rule, Cont.
2:32
Example I: The Empirical Rule
3:24
Z-Score
8:17
Z-Score
8:18
Example II: Z-Score
10:08
Using the Normal Table
13:03
Using the Normal Table
13:04
Using the Normal Table, Cont.
15:05
Example III: Using the Normal Table and Z-score to Calculate Probability
16:01
Step 1: Sketch
16:02
Step 2: Calculate Z-score
18:16
Step 3: Solve for Probability Using the Normal Table
19:14
Example IV: Using the Normal Table and Z-score to Calculate Probability
20:29
Step 1: Sketch
20:30
Step 2: Calculate Z-score
21:52
Step 3: Solve for Probability Using the Normal Table
22:36
Example V: Using the Normal Table and Z-score to Calculate Probability
27:20
Step 1: Sketch
27:42
Step 2: Calculate Z-score
28:14
Step 3: Solve for Probability Using the Normal Table
29:45
Example VI: Using the Normal Table and Z-score to Calculate Probability
34:00
Step 1: Sketch
34:01
Step 2: Calculate Z-score
35:48
Step 3: Solve for Probability Using the Normal Table
36:56
Example VII: Using the Normal Table and Z-score to Calculate Probability
41:21
Step 1: Sketch
41:22
Step 2: Calculate Z-score
44:15
Step 3: Solve for Probability Using the Normal Table
47:26
Example VIII: Calculate the Standard Deviation of the Random Normal Variable
49:54
Step 1: Sketch
49:55
Step 2: Calculate Z-score
51:16
Step 3: Solve for Standard Deviation
53:16
Example VIII: Calculate the Mean of the Distribution
55:11
Step 1: Sketch
55:12
Step 2: Calculate Z-score
56:36
Step 3: Solve for Mean
57:42
Section 6: Distribution of Data
Sampling Distributions

38m 27s

Intro
0:00
Objectives
0:07
Parameter vs. Statistics
0:25
Parameter vs. Statistics
0:26
Sampling Distribution
2:03
Sampling Distribution
2:04
Central Limit Theorem
3:15
Central Limit Theorem
3:16
Central Limit Theorem, Cont.
7:23
Example I: Sampling Distribution Graph
9:20
Conditions (RIN)
11:12
Random
11:13
Independent
12:04
Normal
13:40
Sampling Distribution of a Sample Mean
15:19
Sampling Distribution of a Sample Mean
15:20
Example II: Calculate the Mean and SD of a Sampling Distribution
17:17
Sampling Distribution of a Sample Proportion
21:07
Sampling Distribution of a Sample Proportion
21:08
Example III: Mean, SD, Sample Size, and Probability of a Sampling Distribution
22:29
Part A: Calculate the Mean and SD of a Sampling Distribution
22:30
Part B: Sample Size
26:18
Part C: Probability
29:30
Example IV: Probability of a Sampling Distribution
33:40
Part A: Probability of a Random Selection
33:41
Part B: Probability of the Mean
35:46
Section 7: Statistical Inference
Confidence Intervals

56m 37s

Intro
0:00
Lesson Overview
0:07
Why Calculate a Confidence Interval?
0:28
Using a Statistic to Estimate a Parameter
0:29
What is a Confidence Interval?
1:24
Confidence Interval
1:25
General math Behind a Confidence Interval
2:51
Point Estimate
2:52
Critical Value
4:34
Z-Table
6:06
Z-Table
6:07
T-Table
7:07
T-Table
7:08
General math Behind a Confidence Interval
7:50
Point Estimate
7:51
Critical Value: Mean & Proportion
8:00
Standard Error: Mean & Proportion
8:15
Calculating Using Your Calculator
10:46
Steps to Calculating a Confidence Interval
12:09
Step 1: Read
12:10
Step 2: Check Your Conditions
12:58
Step 3: Calculate
15:33
Step 4: Interpret
16:12
Example I: Confidence Interval
16:29
Example II: Confidence Interval
29:57
Example III: Confidence Interval
42:31
Hypothesis Testing

1h 12m 16s

Intro
0:00
Lesson Overview
0:07
Why do a Hypothesis Test?
0:29
Using a Statistic to Test a Claim about a Parameter
0:30
Steps for Calculating a Hypothesis Test
1:13
1. Write the Hypothesis
1:14
2. Check Conditions
1:30
3. Calculate the Test Statistic
1:34
4. Look Up the P-value & Interpret
1:49
5. Interpret
1:50
Example I: Hypothesis Testing Step by Step
2:57
1. Write the Hypothesis
5:04
2. Check Conditions
8:43
3. Calculate the Test Statistic
21:54
4. Look Up the P-value
20:07
5. Interpret
23:45
Example II: Hypothesis Testing Step by Step
28:49
1. Write the Hypothesis
28:50
2. Check Conditions
32:00
3. Calculate the Test Statistic
34:20
4. Look Up the P-value
38:26
5. Interpret
40:49
Example III: Hypothesis Test for a Mean
44:53
Example IV: Hypothesis Test for a Proportion
57:26
The T Distribution

41m 40s

Intro
0:00
Lesson Overview
0:07
When Do We Use the T Distribution
0:26
When Do We Use the T Distribution
0:27
What is the T Distribution?
1:46
What is the T Distribution?
1:47
Confidence Interval Example
2:49
Construct and Interpret a 90% Confidence Interval to Estimate the Mean
2:50
Hypothesis Test Example
16:59
1. Write the Hypothesis
17:00
2. Check Conditions
20:01
3. Calculate the Test Statistic
21:24
4. Look Up the P-value
24:39
5. Interpret
27:23
Matched Pairs T-test
29:34
Matched Pairs T-test
29:35
1. Write the Hypothesis
33:05
2. Check Conditions
34:58
3. Calculate the Test Statistic
35:52
4. Look Up the P-value
38:12
5. Interpret
39:28
Two Samples

1h 27m 23s

Intro
0:00
Lesson Overview
0:09
What Will a 2 Sample Problem Look Like?
0:40
Example 1
0:41
Example 2
2:01
Writing Your Hypothesis
3:36
Writing Your Hypothesis
3:37
Hypothesis Test Example I
7:02
1. Write the Hypothesis
7:03
2. Check Conditions
10:04
3. Calculate the Test Statistic
13:21
4. Look Up the P-value
20:54
5. Interpret
22:48
Hypothesis Test Example II
24:50
1. Write the Hypothesis
24:51
2. Check Conditions
28:34
3. Calculate the Test Statistic
29:46
4. Look Up the P-value
36:27
5. Interpret
39:01
Example I: Two Samples Hypothesis Testing
42:11
Example II: Two Samples Hypothesis Testing
53:30
“Pick Your Test” Map
1:10:47
“Pick Your Test” Map
1:10:48
Example III: Reliability Testing
1:18:31
Hypothesis Testing of Least-Squares Regression Line

53m 49s

Intro
0:00
Lesson Overview
0:10
Review of Least-squares Regression and Interpretation
0:29
Correlation Coefficient ( r )
0:30
Equation of the Least-squares Regression Line
1:02
Example
2:45
Part A: Least-squares Regression Line
2:46
Part B: Slope of the Least-squares Regression Line
6:03
Test for the Regression Line
7:50
Is There a Correlation?
7:51
Is the y-intercept = 0?
9:56
Conditions for Hypothesis Testing
10:49
Linearity
11:27
Constant Variability
12:35
Normality
13:40
Independence
15:16
Hypothesis Testing
16:10
Standard Deviation of the Residuals
16:11
Standard Error of Slope
17:30
Test Statistic
18:45
Confidence Interval
19:36
Example: Hypothesis Testing
20:45
Part A: Test the Hypothesis
20:46
Part B: 95% Confidence Interval of the Slope
32:51
Interpreting Computer Output
35:40
Interpreting Computer Output
35:41
Example I: Interpreting Computer Output
38:46
Part A: Least-squares Regression Equation
38:47
Part B: Standard Error
40:01
Part C: Slope of the Least-squares Regression Line
41:21
Part D: Null and Alternative Hypotheses
42:08
Part E: Value of Test Statistic
43:09
Part G: P-Value
44:03
Part H: Is Income Useful for Predicting the Cost of a Person’s Car?
45:46
Part I: Estimated Cost
46:57
Example II: Interpreting Computer Output
47:48
Hypothesis Tests for Categorical Data (Chi-Squared Tests)

1h 12m 55s

Intro
0:00
Lesson Overview
0:11
How Do We Know to Use a Chi-Squared Test?
0:27
Categorical Data
0:28
Chi-Squared Goodness of Fit Test
1:50
One Categorical Variable with Counts in Each Category
1:51
What We Have Seen
2:17
New Question Type
2:56
Example I: Chi-Squared Goodness of Fit Test
4:02
Chi-Squared Goodness of Fit Steps Overview
4:03
Step 1: Hypothesis
5:54
Step 2: Expected
7:42
Step 3: Conditions
10:34
Step 4: Calculate
11:44
Step 5: P-Value & Chi-Square Distribution Table
17:03
Example II: Chi-Squared Goodness of Fit Test
22:04
Step 1: Hypothesis
22:05
Step 2: Expected
24:55
Step 3: Calculate
29:05
Step 4: P-Value & Chi-Square Distribution Table
33:18
Chi-Squared Test of: Homogeneity or Independence/Association
34:31
Homogeneity
34:32
Independence/Association
35:42
Example III: Chi-Squared Test of: Homogeneity or Independence/Association
37:55
Step 1: Hypothesis
37:56
Step 2: Expected
40:28
Step 3: Conditions
46:48
Step 4: Calculate
47:49
Step 5: P-Value & Chi-Square Distribution Table
49:30
As a Test of Association
52:53
As a Test of Association
52:54
Example IV: Chi-Squared Test of: Homogeneity or Independence/Association
55:05
Step 1: Hypothesis, Expected, and Conditions
55:06
Step 2: Calculate
59:45
Step3: P-Value & Chi-Square Distribution Table
1:01:51
Example V: Chi-Squared Test of: Homogeneity or Independence/Association
1:02:48
Step 1: Hypothesis
1:02:49
Step 2: Expected and Conditions
1:05:12
Step 3: Calculate
1:06:36
Step 4: P-Value & Chi-Square Distribution Table
1:10:50
Section 8: AP Practice Test
Practice Test 2013 AP Statistics

1h 2m 57s

Intro
0:00
Question 1
0:23
Question 1: Part A
0:24
Question 1: Part B
2:10
Question 2
6:16
Question 2: Part A
6:17
Question 2: Part B
10:22
Question 2: Part C
12:09
Question 3
14:30
Question 3: Part A
14:31
Question 3: Part B
18:19
Question 4
24:49
Question 4: Part A
24:50
Question 5
37:27
Question 5: Part A
37:28
Question 5: Part B
42:32
Question 6
51:15
Question 6: Part A
51:16
Question 6: Part B
55:17
Practice Test 2014 AP Statistics

1h 7s

Intro
0:00
Question 1
0:32
Question 2
9:46
Question 2: Part A
9:47
Question 2: Part B
12:28
Question 2: Part C
13:22
Question 3
15:38
Question 3: Part A
15:39
Question 3: Part B
18:40
Question 4
27:33
Question 4: Part A
27:34
Question 4: Part B
30:05
Question 5
34:15
Question 5: Part 1
34:16
Question 5: Part 2
37:29
Question 5: Part 3
39:50
Question 5: Part 4
40:59
Question 5: Part 5
44:09
Question 6
45:30
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Lecture Comments (3)

1 answer

Last reply by: Sandahl Nelson
Wed Jan 17, 2018 12:37 PM

Post by Reem Alzaabi on December 10, 2017

Can you please explqin the Power of a Test?

0 answers

Post by Reem Alzaabi on December 10, 2017

amazing video
THANKS!!

Hypothesis Testing

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  • Intro 0:00
  • Lesson Overview 0:07
  • Why do a Hypothesis Test? 0:29
    • Using a Statistic to Test a Claim about a Parameter
  • Steps for Calculating a Hypothesis Test 1:13
    • 1. Write the Hypothesis
    • 2. Check Conditions
    • 3. Calculate the Test Statistic
    • 4. Look Up the P-value & Interpret
    • 5. Interpret
  • Example I: Hypothesis Testing Step by Step 2:57
    • 1. Write the Hypothesis
    • 2. Check Conditions
    • 3. Calculate the Test Statistic
    • 4. Look Up the P-value
    • 5. Interpret
  • Example II: Hypothesis Testing Step by Step 28:49
    • 1. Write the Hypothesis
    • 2. Check Conditions
    • 3. Calculate the Test Statistic
    • 4. Look Up the P-value
    • 5. Interpret
  • Example III: Hypothesis Test for a Mean 44:53
  • Example IV: Hypothesis Test for a Proportion 57:26
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