STAT 509 Practice Final Spring 2010
_
Name:
Show work unless specified otherwise. Answers alone will not receive credit. Good Luck.
(1) Below is a stem & leaf diagram for final exam scores from a previous semester. The data has been ordered
and there are
Discrete Random Variables
Sections 3.2 and 3.3
Numeric Random Variables
The numerical outcome of a random circumstance is called a random variable.
Random variables are variable because they keep changing values.
Random variables are random because we don
STAT 509 Practice Final Spring 2010
_
Name:
Show work unless specified otherwise. Answers alone will not receive credit. Good Luck.
(1) Below is a stem & leaf diagram for final exam scores from a previous semester. The data has been ordered
and there are
Introduction to
Engineering Statistics
We must draw conclusions from
partial information.
What
What time should I leave to make it on time to
class?
How
How many hours do we guarantee a light bulb
will operate?
Will
Will the pen caps fit the pen barrels?
Hypothesis Testing
Basic Idea
Interested in testing a claim.
State hypothesis
Use sample evidence and probability to test claims regarding a characteristics of one or more
populations
Steps in Hypothesis Testing
0.
1.
2.
3.
4.
Check Assumptions
State Hypo
Estimation of Proportions
Point Estimate
For a large enough sample, size, the sampling distribution of follows a normal distribution.
(1-)x100% Confidence Interval
z
2
1
n
Example. Historically, 10% of homes in Florida have radon levels higher than recomm
Estimation of the Mean
Point Estimators
A point estimator is a single number calculated from sample data that is used to estimate
the value of a parameter.
Recall that statistics change value upon repeated sampling of the same population while
parameters
Inference for Two Independent Samples
The goal is compare two means for two independent samplesgroups are independent.
Assumptions
We have two samples from independent populations.
We will assume samples came from normal populations.
Examples
Treatment vs
Inferences on Variance
Sample Variance, s2
s2 is the most efficient point estimator for 2 when a sample of size n is drawn from a normal
population.
What do we know about the distribution of s2?
follows a chi-squared distribution with n-1 degrees of freed
Multiple Linear Regression
Models the relationship between many quantitative variables
If we can model the relationship between two quantitative variables, we can use a set of variables, Xs, to
predict another variable, Y.
Example. Reaction time of brakin
M ultiple Regression Examples
1.
A study of gas turbine engines, found that during the hot summer months, the power
output from these engines dropped dramatically. One way to counter this drop in power is
by cooling the inlet air of the turbine. The heat
Control Chart Examples
Problem 5.14. A chemical engineer supervises a new distillation column. Five times each shift, she determines
the yield from the column. Table 5.8 lists the yields for 20 shifts.
a.
Calculate the appropriate control limits for an R-
11/23/2009
Introduction to
Factorial-Based
Experiments
The 2 Factorial Design
Uses 2 factors that are thought to influence a
single response variable.
Ex. The effect of reaction temperature and
pressure on the strength of polymer fibers.
Chapter 7.1
Eac
Control Charts
Principles of Statistical Thinking
All work occurs in a system of interconnected processes,
Variation exists in all processes, and
Understanding and reducing variation are the keys to success.
Control Charts
Processes include equipment, mat
2k F actoria l Analysis Examples
7.12 Shina (1991) conducted an experiment to determine the impact of wave width (x1),
d irection (x2), f lux (x3), and angle (x4) on the average number of short leads per batch
p roduced by a wave-soldering process for pri
Sixsigma
Introduction
Click to edit Master subtitle style
All Rights Reserved TreQna 2005
expectations
Click to edit Master subtitle style
All Rights Reserved TreQna 2005
Awarenesswithrespectto
originandhistoryofSix
Sigma.
Theutilityandbenefits
Introduc
STAT 509 Final Exam Thursday April 29th at 5:30 pm in LeConte
412
Data Displays
In terpretation of histogram, stem & leaf and boxplot
5 number summary, percentiles, mean, std dev, variance, outliers
Discrete Random Variables
Calculating probabilities, exp
Simple Linear Regression
Modeling the Relationship Between Two Quantitative Variables
If we can model the relationship between two quantitative variables, we can use one variable, X, to
predict another variable, Y.
o Use height to predict weight.
o Use pe
Formula Sheet
Exponential Distribution
exp
0
0
Uniform Distribution
Normal Distribution
Test Statistics for Hypothesis Testing
Parameter
Mean
Test Statistic
Mean
Proportion
z
p
p
1
n
*You will be asked to interpret other hypothesis tests but youll be give
Chapter 2: Descriptive Statistics
Ways to summarize data
Numerically
Graphically
Example: Consider the top driving speeds of students from a large statistics class:
sider
Whats the strata?
Descriptive Statistics
Page 1
Stem & Leaf Diagram
Popular method t
Basic Probability
Definitions
Probability represents a (standardized) measure of chance, and quantifies uncertainty.
Let S = sample space which is the set of all possible outcomes.
An event is a set of possible outcomes that is of interest.
If A is an eve
Discrete Random Variables
Sections 3.2 and 3.3
Numeric Random Variables
The numerical outcome of a random circumstance is called a random variable.
Random variables are variable because they keep changing values.
Random variables are random because we don
Continuous Random Variables
Sections 3.4 to 3.5
Continuous Random Variable
A continuous random variable is one for which the outcome can be any value in an interval
of the real number line.
Examples
Let Y = length in mm
Let Y = time in seconds
Let Y = tem
Random Behavior of Means
Goals
We want to estimate characteristics about a population using a sample
We can Estimate Population Characteristics with Relatively Small Samples
Step one is to select a random sample from the population of interest.
Random Sam