ENME392 Fall 2011
Homework 9 Solutions
Total number of points: 100
Assignment:
1.
The following data were collected for the number of M&Ms of each color in 17 small
bags of candies.
(20 pts)
a) What is the probability that the red data could have come fro

SAMPLING CONFIDENCE INTERVALS
1. WHAT IS THE CENTRAL LIMIT THEOREM? (IN YOUR OWN WORDS) WHAT
ARE THE RULES FOR IT? EXPLAIN WHY YOU THINK IT WORKS. IN OTHER
WORDS HOW IS IT POSSIBLE THAT YOU CAN HAVE A UNIFORM
DISTRIBUTION OR AN EXPONENTIAL ONE AND BOTH WI

Statistical Process Control
1
Statistical Process Control (SPC)
A process must be checked to see if it meets specification limits
Statistical process control means that the process must also be
consistent.
Essentially, SPC is
Confidence intervals that

Estimation and Sampling
Understanding the basic principles behind the
use of samples to understand populations
1
Overview
Definitions: Population, Sample, Statistic, Point
Sample mean &
Estimation, Sampling distribution ,
variance.
Population statistic

Joint Probability Distributions
Calculating and working with joint probabilities
and systems with more than one random
variable
1
Recap(itulation)
How to count
Sample spaces, Permutations, Combinations, Addition & Multiplication
Rules, Independence, Mut

Two-Factor ANOVA
1
Two-Factor ANOVA
In the previous slides, the 2nd factor was not of interest. What if it is?
What if you want to study the effect of two parameters (factors) at several levels
on an outcome?
4 types of steel and 5 formation temperatures

Discrete Random Variables and
Discrete Probability Distributions
Understand how discrete probability distributions are
developed and how they are used/analyzed
1
Recap(itulation)
How to count
Sample spaces, Permutations, Combinations, Addition & Multipl

Continuous Random Variables and
Continuous Probability Distributions
Understand how continuous probability distributions
are developed and how they are used/analyzed
1
Recap(itulation)
Last time:
Discrete Variables and Discrete Distributions (Probabilit

Statistical Inference Techniques
- Two samples (Parametric)
- Nonparametric testing
1
Overview
Other kinds of useful two-sample tests using chi-squared
Goodness of Fit
Independence
Homogeneity
Other kinds of useful (hypothesis) tests for non-normal
d

ENME392 Fall 2011
Homework 4 Solutions
Total number of points: 100
1.
Chapter 3: 3.39 (leave as a formula)
(4 pts)
sack of fruit with 3 oranges X, 2 apples Y, 3 bananas B
8 total fruit, take 4 pieces
X = # oranges, Y = # of apples
(a) f(x,y) = ?
same as e

ENME392 Fall 2011
Homework 5 Solutions
Total number of points: 100
Assignment:
1.
Chapter 8: 8.22
(5 pts)
(a) the mean and standard deviation of the sampling distribution
cm
cm
(b) The number of sample means that fall between 172.5 and 175.8 cm:
mean samp

ENME392 Fall 2011
Homework 6 Solutions
For this problem, you may work in groups of up to 4. Obtain a box or box lid of
approximately 9 x 13. Draw a square on the bottom of it that is 3.5 on each side; the
square can be off center. From a height of approxi

ENME392 Fall 2011
Homework 7 Solutions
Total number of points: 100
The questions are a follow-up to last-weeks assignment: (80 pts)
a) Group your number-of-heads data into 25 groups of 4 points by taking the results of the
first 4 tosses, then the next 4,

ENME392 Fall 2011
Homework 8
Total number of points: 100
The question is a follow-up to last-weeks assignment:
a) What is the 95% prediction interval for a future number of heads?
(8pts)
Textbook problems:
1.
Chapter 9: 9.18 (Edition 8) / 9.14 (Edition 9)

ENME392 Fall 2011
Homework 11 Solutions
Total number of points: 100
1. Chapter 10: 10.84 (Edition 8) / 10.82 (Edition 9)
(10 pts)
The hypotheses are
H0 : Data follows the hypergeometric distribution h(x; 8, 3, 5),
H1 : Data does not follows the hypergeome

ENME392 Fall 2011
Homework 13 Solutions
Total number of points: 100
1. Chapter 13: 13.28 (Edition 8) / 13.26 (Edition 9)
(10 pts)
The hypotheses are
H0 : 1 = 2 = 3 = 0, no differences in the varieties
H1 : At least one of the is is not equal to zero.
= 0

ENME392 Fall 2010
Homework 8 Solutions
Total number of points: 48
1.
Chapter 9: 9.36
(3pts)
nA = 50, nB = 50, xA = 78.3, xB = 87.2, A = 5.6, and B = 6.3. It is known that z0.025 =
1.96. So, a 95% confidence interval for the difference of the population me

Regression Analysis:
Linear & Multiple Regression
1
Overview
Regression Analysis is an approach to develop a mathematical
function to describe empirical data using a rigorous procedure to
control approximation error
Types of regression analyses
Linear r

ENME 392, Fall 2015
Statistical Methods for Product and Processes Development
Instructors:
Professor Peter W. Chung
Professor Christopher Chabalko
What is ENME392 about?
Engineers must evaluate new designs, procedures, and materials.
Probability & Statist

Design of Experiments
1
Problem:
- Complex system with known parameters (knobs) and response variables
- Effects of parameters are unknown
- The are the effects of turning the knobs?
2
Introduction
An experiment is a test or series of tests.
The design of

Analysis of Variances (ANOVA)
1
Big Picture
Topics
Confidence Intervals
Hypothesis Testing
Regression
Analysis of Variance
Design of Experiments
These subjects equip you to perform a sequence of activities:
(Every experiment involves this sequence)
1. C