Cumulative Notes AP Statistics
Cumulative Notes AP Statistics
Prepared by: Earl L. Whitney, FSA, MAAA Version 1.0
April 27, 2014
Copyright 2014, Earl Whitney, Reno NV. All Rights Reserved
2
AP Statistics Cumulative Notes Table of Contents
Page Description
6 AP Statistics Formula Sheet
8 Part 1: Exploring Data
8
Variable Types
8
5-Number Summary
8
Other Terms to Know
9
Frequency Distribution
9
Cumulative Frequency Distribution
10
Center, Shape and Spread
11
Types of Plots
13
Marginal Distributions
14
Normal Distribution
15 Part 2: Exploring Bivariate Data
15
Definitions
17
Formulas Relating to the Coefficient of Correlation of a Sample
18
Linear Combinations of Parameters and Statistics
19
Types of Regression Models
20 Chapter 10: Straightening Data In a Scatterplot
20
Selecting a Good Re-Expression Model
22
Re-Expression Models Based on the Scatterplot
23
Re-Expression Models Based on the Residuals
24
Description of Individual Models
30 Chapter 12: Sample Surveys
30
Types of Samples
30
Types of Bias
31
Table of Key Statistics ad Parameters
31
The Valid Survey
32 Chapter 13: Experiments and Observational Studies
32
Observation Study
32
Experiment
32
Principles of Experimental Design
33
Diagramming an Experiment
33
Elements of an Experiment
33
Other Terms Relating to Experimentation
Version 1.0
April 27, 2014
3
AP Statistics Cumulative Notes Table of Contents
Page Description
34 Part 4: Probability
34
Key Definitions
36
Geometric Probability Model
36
Binomial Probability Model
36
Normal Probability Model
37
Key Formulas
38 Chapter 18: Sampling Distribution Models
38
Central Limit Theorem
38
Key Assumptions
39
Symbols and Formulas for Proportions
39
Symbols and Formulas for Population Means
40 Chapter 19: Confidence Intervals for Proportions
40
Explaining a Confidence Interva'
40
Critical Values
40
Standard Deviation vs. Standard Error
40
Key Assumptions
41 Chapter 20: Hypothesis Testing for Proportions
41
Hypotheses
41
P-Value
42
Four Steps of Hypothesis Testing
43
Z-Values and P-Values for Various Tests - 95% Confidence
44 Chapter 21: More About Tests and Intervals
44
a-Value
44
Rules for Rejecting H0
44
b-Value
44
Power
44
Effect Size
45
95% Confidence Interval (When the Success/Failure Condition Fails)
45
Summary of p's and n's
46
Type I and Type II Errors
46
Interaction of a, b, and Power
47 Chapter 22: Comparing Two Proportions
47
Confidence Interval for the Difference of Two Proportions
47
Key Assumptions and Conditions
48
Hypothesis Testing
Version 1.0
April 27, 2014
4
AP Statistics Cumulative Notes Table of Contents
Page Description
49 Chapter 23: Inferences About Means
49
Sample of Means
49
Confidence Interval for the Difference of Two Proportions
50
Using z vs. t
50
Key Assumptions and Conditions
50
Sample Size for a t-Distribution
50
Special Considerations
50
Language for Confidence Intervals
51
Hypothesis Testing
51
Relationship Between Intervals and Tests
51
Finding the Required Sample Size
51
Finding the Required Sample Size - Example
53 Chapter 24: Comparing Means
53
Boxplots
53
Sample of Means
53
Confidence Interval
54
Key Assumptions and Conditions
54
Sample Size for a t-Distribution
54
Special Considerations
54
Hypothesis Testing
55
Pooled t-Interval and t-Test
56 Chapter 25: Inferences About Paired Data
56
Pairing
56
Sample of Means
56
Confidence Interval
57
Key Assumptions and Conditions
57
Hypothesis Testing
58 Statistical Inference Summary Chart
59 Chapter 26: Comparing Counts ? The Distribution
59
Uses and Characteristics
59
Hypothesis tests
60
Testing Goodness of Fit
62
Testing Homogeneity or Independence
Version 1.0
April 27, 2014
5
AP Statistics Cumulative Notes Table of Contents
Page Description
65 Chapter 27: Inferences for Regression
65
Moel of the Idealized Line
65
Visualization
65
Key Assumptions and Conditions
66
Work Order
66
Calculations
67
Thoughts about the Size of the Standard Error
68
Hypothesis Tests and Confidence Intervals for Linear Regression on the TI-84
Version 1.0
April 27, 2014
6
AP Statistics Formula Sheet
Version 1.0
April 27, 2014
7
AP Statistics Formula Sheet
Version 1.0
April 27, 2014
8
Exploring Data
Variable Types:
A quantitative variable is one that takes on numerical values. Examples: age, weight, salary, GPA, temperature, etc.
A categorical variable is one that is not quantitative. Examples: dog breed, hair color, high school attended, political affiliation, etc.
5-Number Summary (and related terms)
Arrange the quantitative data from low to high. Then:
Minimum: The lowest value.
1st Quartile (Q1): The median of the lower half of the values. Note: if there are an odd number of values, exclude the median from the lower half of the values in calculating Q1.
Median: The middle value. Note: if there are two middle values, the median is the mean of those two values.
3rd Quartile (Q3): The median of the upper half of the values. Note: if there are an odd number of values, exclude the median from the upper half of the values in calculating Q3.
Maximum: The highest value. Interquartile Range (IQR): IQR Q3 Q1
Range: Range Maximum Minimum
Outliers: Values that are more than 1.5 IQR's above Q3 or 1.5 IQR's below Q1. Note: in a Normal Distribution, data are considered outliers if they are more than two Standard Deviations away from the mean. These data are often referred to as "unusual."
unusual
Other Terms to Know
Mean: The arithmetic average of the values.
Mode: The value or values that occur most often.
Cluster: A natural subgroup of data which lie close together.
Gap: A break in the data; i.e., a range where no values exist.
Clusters
Version 1.0
Gaps
April 27, 2014
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.