# Ch. 4-6 PowerPoint Review

```AP Statistics
Semester One
Review
Part 2
Chapters 4-6
AP Statistics Topics
Describing Data
Producing Data
Probability
Statistical Inference
Chapter 4:
Designing
Studies
In this chapter, we learned
methods for collecting data
through sampling and
experimental design.
Sampling Design
Our goal in statistics is often to answer a
question about a population using information
from a sample.
to do this, the sample must be representative
of the population in question
Observational Study vs. Experiment
If you are performing an
observational
study,
Sampling
obtained in a number of
ways:
Convenience Sample
Simple Random
Sample
Stratified Random
Sample
Systematic Random
Sample
Experimental Design
In an experiment, we impose a treatment
with the hopes of establishing a causal
relationship.
3 Principles of Experimental Design
Randomization
Control
Replication
Experimental Designs
Experiments can take a number of different
forms:
Completely Randomized Design
Randomized Block
Design
Matched Pairs Design
Chapter 5:
Probability:
What are the
Chances?
This chapter introduced us to
the basic ideas behind
probability and the study of
randomness.
We learned how to calculate and
interpret the probability of
events in a number of different
situations.
Probability
Probability is a measurement of the
likelihood of an event. It represents the
proportion of times we’d expect to see an
outcome in a long series of repetitions.
Probability
Rules
The following facts/formulas are helpful in
calculating and interpreting the probability of an
0event:
≤ P(A) ≤ 1
P(SampleSpace) = 1
P(AC) = 1 - P(A)
P(A or B) = P(A) + P(B) - P(A and B)
P(A and B) = P(A) P(B|A)
A and B are independent if and only if
P(B) = P(B|A)
Strategies
When calculating probabilities, it helps to
consider the Sample Space.
List all outcomes, if possible
Draw a tree diagram or Venn diagram
Sometimes it is easier to use common
sense rather than memorizing formulas!
Chapter 6:
Random
Variables
This chapter introduced us
to the concept of a random
variable.
We learned how to describe
an expected value and
variability of both discrete
and continuous random
variables.
Random Variable
A Random Variable, X, is a variable
whose outcome is unpredictable in the
short-term, but shows a predictable
pattern in the long run.
Discrete vs.
Continuous
Expected Value
The Expected Value, E(X) = &micro;, is the
long-term average value of a Random
Variable
E(X) for a Discrete X
Variance
2
σ,
The Variance, Var(X) =
is the amount of
variability from &micro; that we expect to see in X.
The Standard Deviation of X,
Var(X) for a Discrete X
Rules for Means and Variances
The following rules are helpful when
working with Random Variables.
Linear
Transformations on
Random Variables
Sums &amp; Differences
of Random Variables
Some
Random Setting
Variables are the result of
Binomial
events that have only two outcomes
(success and failure). We define a Binomial
Setting to have the following features:
Binary Situations (Two Outcomes success/failure)
Independent trials
Number of trials is fixed - n
Probability of success is equal for each
trial
IfBinomial
X is B(n,p), the
following formulas can be
Probabilities
used to calculate the probabilities of events
in X.
The mean and standard deviation of a
binomial distribution simplifies to the
following formulas:
Some Random Variables are the result of
Geometric
Setting
events that have only two outcomes
(success and failure), but have no fixed
number of trials. We define a Geometric
Setting to have the following features:
Binary Situations (Two Outcomes success/failure)
Independent trials
Trials continue until a success occurs
Probability of success is equal for each
trial
Geometric
Probabilities
If X is Geometric, the following formulas can
be used to calculate the probabilities of
events in X.
The mean of a geometric distribution
simplifies to the following formula:
Semester One
Final Exam
50 Questions
Multiple Choice
Chapters 1-6
Tuesday and Wednesday
```