Probability Cheat Sheet (The Legal Version!) Basic Probability Formulas Word Or And Not Operati on Add Multiply Subtract General Rule PAB=P(A)+P(B)-P(AB) PAB=PABP(B) PA'=1-P(A) Special Case, Rule Mutually Exclusive, PAB=P(A)+P(B) Independent, PAB=P(A
JMP Notes
(A Quick Reference Supplement to the JMP Users Guide)
These notes outline the JMP commands for various statistical methods we will discuss in class (and then some). Dont worry if
you dont understand technical terms like variance inflation factor
Chapter 4
SECTION 4.3
4.3 Hypothesis testing for a single mean with unknown variance
Recall: Variance known:
One-sided Z-tests
Two-sided Z-tests
Variance unknown:
One-sided t-tests
Two-sided t-tests
4.3.1 One sided t-tests
Consider the injection molding p
Chapter 4
SECTION 4.4
4.4 Tests for Proportions
When randomly sampling from a population with proportion p of
successes, the sampling distribution of the sample proportion p [p hat]
has mean and standard deviation:
p = p
p p
p =
p(1 p)
n
is an unbiased
Stat 3704: Stats for Engineering
Applications
Introduction/Chapter 1
1
Engineering Method
The heart of sound engineering practice is the engineering
method
2
Example: Strength of Filament
Consider a production process of a new kind
of filament. In the pro
Chapter 3
SECTION 3.2 3.3
3.2 Random Variables and Distributions
Random Variable: Y is a random variable if Y is a function that assigns a
real numbered value to every possible event in a sample space, S, of
interest
Use capital letters to denote random
Stat 3704: Stats for Engineering
Apps
1
CHAPTER 2: DATA DISPLAYS
Overview
2
Stemplot
Boxplot
Histogram
Time Plots
Introduction
3
What do we actually do with a data set when its
handed to us?
By observing visual summaries of the data, we can:
Determ
Stat 3704: Stats for Engineering
Apps
CHAPTER 3: MODELING RANDOM
BEHAVIOR
Overview: Probability
2
Statisticians use probability to model uncertainty.
Consider-these statements:
There is a 30% that our engineering design firm will get the Nissan
contract.
Box Plots
1
Purpose: To give a quick display of some important features
of the data.
Note: The box plot represents a distillation of the data.
The stem-and-leaf display only loses the time order of the
data.
The box plot loses some of the information
Tuesday, March 13, 2012
2:05 PM
Review Five-step Testing
1.
2.
3.
4.
5.
State the hypothesis
State the test statistics
State the critical region
Conduct the experiment and find Z
Reach conclusions and state them in English
EX. (One sided Z test)
X1, X2.X9
Tuesday, February 21, 2012
2:04 PM
Method of Moments (MME)
If there is only on e parameter
E(x)
If there are two parameters
E(x) =
Var(x) = S^2
Statistics Page 1
Statistics Page 2
Statistics Page 3
Hypothesis Testing
Thursday, March 01, 2012
2:03 PM
Def: A hypothesis is a statement about a population parameter.
Null Hypothesis: H0:mu = 100
Alternative hypothesis Ha
mu = 100
Two sided Ha > 100
One sided Ha < 100
H0 = 100
Ha > 100
Type I error
Reject
Thursday, February 09, 2012
2:07 PM
Def: F(x) P(X=<x) is called the cumulative distribution function (df) of X
F(1) = F(2) = . = F(6) = 1/6
Discrete random variable
Def: A discrete random variable is one that can assume at most a countable number of value
Conditional probability and independence
Tuesday, February 07, 2012
2:00 PM
In some random experiment we are interested in those outcomes that are elements of a subset of C1 of the
sample space S.
We take C1 to be the new sample space and want to define t
Stat 3704: Statistics for Engineering Applications
Midterm2 - Sample Test
Part I Multiple Choice & Short Answer
Please write down your answers in the Answer Table! Only answers in the Answer Table
will be accepted.
Answer Table
1.
2.
3.
4.
5.
6.
1. A clot
Using Your TI-83/84/89 Calculator for Hypothesis Testing:
The 1-Proportion z Test
Dr. Laura Schultz
Statistics I
The 1-proportion z test is used to test hypotheses regarding population proportions. This handout
will take you through one of the examples we
STAT 3704: STATS FOR
ENGINEERING APPS
Chapter 2: Data Displays
Introduction
What do we actually do with a data set when its handed
to us?
By observing visual summaries of the data, we can:
Determine the general pattern of data
Identify outliers
Check
Statistical Inference I
STAT 3704
~4.1, 4.2
Overview
Reason for Inference
Parameter Estimation
Hypothesis Tests
Confidence Intervals
Summary
Reason for Inference
Last chapter, we worked on probability problems.
We identified an appropriate distribu
Lecture 10: Simple Linear
Regression
STAT 3704
Sections 6.1, 6.2
Introduction
Scatter Plots and Association
Model and Assumptions
Estimating the Parameters
Residuals
Measures of Model Usefulness
Summary
One important topic to engineers is to fit
m
STAT 3704
Sections 3.3-3.5
Introduction
Discrete vs. Continuous
Expected Value and Variance
Common Discrete Distributions
Common Continuous Distributions
The Normal Distribution
Summary
2
Last time, we introduced the idea of random
variables, whic
Inference for Variances
Stat 3704
Sections _
Overview
n
n
n
n
Introduction
Comparing a Variance
Comparing Two Variances
Conclusions
Inferences for Variances
n
n
For the last several lectures, we ve been
focused on making inferences about
pop
STAT 3704
Sections 3.6-3.7
Introduction
Sample Average and Variance
Central Limit Theorem
When Variance is Unknown
Q-Q Plots
Summary
2
Last time, we talked about a whole host of
common distributions for random variables.
This list may have seemed
Inference for Means from
Two Samples
Stat 3704
Sections 4.5 & 4.6
Overview
n
n
n
n
Introduction
Independent Samples
Paired Samples
Conclusions
Two Sample Means
n
In the last lecture, we learned how to use
t-tests (or z-tests for large sam
Inference for a Single Mean
STAT 3704
~4.3
Overview
Introduction
Hypothesis Test
Confidence Interval
Summary
2
Introduction
Consider a situation where we want to estimate the mean
value of a population.
For example, in our marble factory, the diamet
Al @Oneway Analysis of Data By group
74 I
T3
Data
'.-'2
TI
70 0
groun
JQuantiles
Level Minimum 10% 25% Median T555 90% Maximum
1 70 70 72 72.5 T3 74 74
2 TO 70 TI 72 72 74 T4
Name Kg period12345678
AP Stats Ch 9 Testing a Claim. Practice Multiple Choice
1. ln formulating hypotheses for a statistical test of signicance, the null hypothesis is often
a statement 0 no effect or no difference.
B. the probability of observing the d
STAT 3704: Statistics for Engineering Applications, Fall
2016
Practice Exam 2
Use the following to answer Questions 1 2.
A national survey interviewed 3800 people ages 18 and older nationwide by
telephone. One question asked was the amount of gasoline the
Chapter 4
SECTION 4.2
Review: The process to get CI for a population mean ( known)
1. Check the simple conditions.
- The sample is simple random sample(SRS).
- Sample size is large enough to assume CLT.
- The mean is unknown but the standard deviation is
Chapter 4
SECTION 4.1
4.1 Introduction to Estimation
p
p
Population: the set of all
possible observations of
interest to the problem at
hand.
Sample: the part of the
A parameter is a numeric
quantity that describes an
important characteristic of a
popula