APMA 311
Monday, November12, 2007
APMA 311 Test 2
Section: _
Name: _
Directions: This test is four pages long, not including the cover sheet.
Show your work on all problems to obtain full creditcircle your final answer.
You may use your calculator, a half

Section 5.1
Confidence Intervals
Reporting Uncertainty in Estimation
1
Motivation
Consider X as a point estimator of
If repeated samples are taken,
what values do we expect to see in x ?
i
5.1
J. Maybee, UVa, 2009
2
Consider a RS from a normal populatio

Section 2.1
Probability Concepts
How can we understand chance?
1
Basic Concepts
i Experiment : A process that results in an outcome
that is governed by chance
i
i Sample space : The set of all possible outcomes
of an experiment
2.1
J. Maybee, UVa, 2009
2

Section 1.1
Sampling
Basic Concepts
1
Statistics
i Applicable to all aspects of life
i Involves collection, analysis, and interpretation
of uncertain data
Probability concepts provide foundation
i Methods involve design of experiments that allow
reliable

APMA 311 Practice Problems
Linear Regression and ANOVA
1. In material science, one often performs stress tests on rods made from new experimental alloys. The
following data are the longitudinal strain (X) and lateral strain (Y) from 10 experiments:
X (lon

Section 3.1
Propagation of Error
Measurement Error
1
Measurement Errors
Any measuring procedure contains error
Calculations based on msmts propagate the error
(from msmt to calculated value)
i
3.1
J. Maybee, UVa, 2009
2
Extended Model
Measured Value = Tr

Section 4.1, 4.2
Commonly Used Distributions
Bernoulli and Binomial
1
Probability Distributions
Key Characteristics of pmf and pdf
i Probabilities are 0
i Sum = 0
May be derived from
i Idealized processes/mathematical rules
i
4.1, 4.2
J. Maybee, UVa, 200

Section 4.11
Sampling Distributions and The
Central Limit Theorem
1
Sampling Distributions
i Any statistic calculated from a random sample
is a random variable (e.g., X and s 2 )
i The probability distribution of a statistic is called
its sampling distrib

Problem 1
Fortyfive specimens of a certain type of powder were analyzed for sulfur trioxide content. The results
are shown below, in percent. The list has been sorted into numerical order. Using Minitab 17 or another
statistical software package, perform

Carolyn Diamond
Problem 1
Do the data appear to come from an approximately normal distribution? Yes,
the data appear to be a good fit for the normal probability distribution as it is
tight to the line.
Problem 2
Do the data appear to come from an approxim

APMA311 Applied Probability and Statistics
Spring 2009
HOMEWORK ASSIGNMENT: 3
Due: At the start of Class on Wednesday, February 4th
Readings and Assigned Problems (even numbers)
2.3 Bayes Rule and Reliability
22 26, 30, 32
2.4 Random Variables
2 10, 14
2.

APMA311 Applied Probability and Statistics
Spring 2009
HOMEWORK ASSIGNMENT: 2
Due: At the start of Class on Wednesday, January 28th
Readings and Assigned Problems (even numbers)
2.1 Basic Probability Ideas
2, 6 10, 14 18
2.2 Counting Methods
2 10
2.3 Cond

APMA311 Applied Probability and Statistics
Spring 2009
HOMEWORK ASSIGNMENT: 1
Due: At the start of Class on Wednesday, January 21st
Readings and Assigned Problems (even numbers)
1.1 Sampling
26
1.2 Summary Statistics
2 10, 14 16
1.3 Graphical Summaries
2*

Applied Probability and Statistics, APMA311
Probability Handout
INTRODUCTION TO PROBABILITY
Example Problems
Alternative Formulations
A class has 12 boys and 4 girls. If 3 students are selected at random from the class, what
is the probability that they a