Physics 1C Winter 2013:
Final
1
Version A: Closed book. No work needs to be shown for multiple-choice questions. You may
use a calculator. All values are in SI units unless explicitly stated otherwise.
1. A13gmasshangsfromaspringinearthsgravitysothatthefo
Chapter 14
Analysis of Variance for CR Designs
Lecture 1 Completely randomized
design w/ one factor
1
1. Example: # cereal cases sold (10 stores)
- Response: number of cases of cereal sold
- Treatment: design of the cereal package, 4 levels
- Cereal is s
Statistics 350A
The level of significance or p-value of a statistical test
(Section: 5.6)
1
Definition:
p-value is the probability of observing a sample that is
at least as contradictory to H0 as the sample at hand, if
H0 is true. The smaller the p-value,
IV Chapter 8
Lecture 1
Introduction to ANOVA
1
Chapter 8 - Inference comparing more than
two population means: analysis of variance
(ANOVA)
An extension of 2-independent sample t-test
2
1. 2-sample t-test
H0: 1= 2
Assumptions:
1. Random samples
2. Ind
Statistics 350A
.
Illustration :
Let's say we are interested in learning the population
mean height of Stat 350A students.
Let's take samples of 2:
Random
Sample
Height 1
Height 2
1
74"
76"
75"
2
65"
69"
67"
3
66"
68"
67"
4
64"
70"
67"
5
63"
73"
68"
Examp
PHYSICS 1C - Fall 2016
FINAL PREPARATION GUIDE
SELECTED HOMEWORK QUESTIONS / PROBLEMS
The subset of suggested homework problems listed below have been selected to
help your best focus your studies for the final exam, but these problems are
NOT meant as a
PHYSICS 1C - Fall 2016
FINAL PREPARATION GUIDE
SELECTED PROBLEMS FROM QUIZZES 1 - 3
The subset of problems from Quizzes 1 -3 listed below have been selected to
help your best focus your studies for the final exam, but these problems are
NOT meant as a gua
Statistics 350A
Normal Approximation to the Binomial Distribution
(Section 4.13)
1
1. Normal approximation to Binomial
Y = Bin(n, ) N(n, n(1-)
if n 5 and n(1-) 5
2
a
2. The normal approximation to the binomial
distribution is an application of the CLT. Wh
Chapter 13
Model building & diagnostics
Lecture 1
Model section criteria and variable
selection methods
1
Multiple linear regression model:
yi = 0 + 1 xi1 +. + k xik + i
i = 1,., n
Assumptions : i are independent
2
i ~ N(0, )
2
1. Model selection crit
Introduction to ANOVA
Transformations
(Section 8.5)
1
Assumptions in ANOVA
indep
2
~ N (0, )
Constant variance
residual analysis
Normality
2
Transformations on y to stabilize variances ( 8.5)
2 is proportional to (count data,
or s2 / Y is a constant
Statistics 350A
Assessing Normality
(Section 4.14)
1
1. Using the Empirical Rule
Empirical Rule:
For bell-shaped data
The interval s contains approximately 68% of the
measurements.
The interval 2s contains approximately 95% of
the measurements.
The interv
Statistics 350A
Normal Distribution
(Sections 4.9-4.10)
1
Normal Distribution
Most important distribution because it approximates to the distribution
of an observed variable Y in many applications
Example
Cholesterol levels
SAT scores
The yearly rainfa
Chapter 15
ANOVA for blocked designs
Lecture 5 Factorial experiment in a
RCB design
1
CR design homogeneous population
RCB design one blocking variable
LS design two blocking variables
Factorial treatments can be applied to each of these
designs
Example:
Statistics 350A
Interpretation of , Sample Size, and Power
(Section 5.5)
1
1.Interpretation of
Fact: When H0 is true (i.e. = 0), by CLT
( - 0)/(/n) ~ N(0, 1), if pop is normal or n is large
2
What we do:
R.R. (for Ha: 0): Reject H0 if |z| z1-/2
3
In hypo
Statistics 350A
Binomial Distribution
(Sections 4.6-4.8)
1
Motivating example
If two carriers of the gene for albinism marry, each of their children has
probability of being albino. If the couple has 3 children, what is the
probability distribution for Y,
Statistics 350A
C.I. and Hypothesis Testing when is unknown
(Section 5.7)
1
CLT: If = 0, (- 0)/(/n) ~ N(0,1), if population
distribution is normal or sample size is large
When is not known, ( - 0)/(s/n) ~ t(n-1), if
population distribution is normal or sa
Statistics 350A
Two Sample Inference: CI for 1-2
(Sections 6.1-6.2)
1
1
1. Notation
1
2
1
2
Population 1
Sample of n1
Population 2
Sample of n2
2
2
2. Sampling distribution of 1 - 2
Sampling distribution of 1
1 ~ N(1, 12/n1), if population 1 is normally
d
Statistics 350A
One Sample Inference: CI and Testing When is Known
(Sections 5.1-5.2, 5.4)
1
1. Techniques of Statistical Inference
a.Point Estimate: a value that serves as the best guess
of the parameter
b.nterval Estimate: an interval of values in which
Statistics 350A
Two Sample Inference: Hypothesis testing concerning 1-2
(Sections 6.1-6.2)
1
Sampling distribution of 1 - 2
1 - 2 ~ N(1-2, 12/n1+22/n2), if both populations are
normally distributed or if both n1 and n2 are large.
2
General form of a test
Chapter 13
Model building & diagnostics
Lecture 3 Transformations
1
Model & assumptions:
yi = 0 + 1 xi1. + k xik + i
i are independent
i ~ N(0, 2 )
Residual : ei = yi yi
model assumptions are satisfied residuals are
randomly distributed around 0, no pat