Mathematics 312
HW01-Math231 Review
Due: 09/05 by 4:00pm
Fall, 2013
1. Which of the following description about P-value is/are CORRECT?
(a) It is the probability for the null hypothesis bing true.
(b) The signicance level is the maximum of P-values for th
MATH 312 Sheet
Wei Zhang
[email protected]
Chapter 10
: number of groups; : number of observations within each group; = = : total number of observations.
Additive Model (Test whether the differences in the sample averages are significant):
= + +
Assumpt
Multiple Comparison
Ping-Shi Wu
Department of Mathematics
Lehigh University
Wu, P. S. (Lehigh University)
Math312 Fall 2016
1/1
Recall in the overall group means comparison:
H0 :
1 = 2 = 3 = = t ,
Ha :
at least one pair of (i, j),1i6=jt , i 6= j .
The nul
Ch.10 ANOVA
Ping-Shi Wu
Cell means model
Recall that we used two-sample t-test to evaluate the significance of
difference between two independent sample means. Here we will learn a
more general way which is called cell means model. With this tool, we can
Fixed Effect Model (FEM)
Ch.11 ANOVA-03
Ping-Shi Wu
Considering the Chain saw example, the inference is about the
comparison among those FOUR specific models. The conclusion
cannot be applied to other models (or general model effects). If
the experiment i
Spearmans rank correlation
1. Steps:
(a) Sort xi s and yi s separately, record their individual ranks in original pair, i.e. (rxi , ryi ).
n
P
(b) Calculate rs =
(rxi
rx )(ryi
ry )
s
n
n
P
P
(rxi
rx )2
(ryi
ry )2
i=1
s
i=1
i=1
n
P
d2i
i=1
n(n2 1)
6
2.
One-way factor effect model
In cell means model, all the groups could correspond to the levels
of a factor. The significant difference among levels would then
reflects the factor effect. Consider the breakdown of level
mean (i ) in the following:
Ch.10 AN
Ch.12 ANOVA-04
Ping-Shi Wu
Department of Mathematics
Lehigh University
Nested Design
In experiments, there is interest in one set of treatments and the
experimental units are measured more than once or are
sub-sampled (from unit population).
Example
3 die
Testing on H0 : = 0
For LARGE sample size (n 25)
1 1 + r
Z = arctanh r = ln
2
1r
Math312-Corr. and Test on Normality
is approximately normal distributed with
Ping-Shi Wu
1 1 +
mean = arctanh = ln
2
1
Department of Mathematics
Lehigh University
and varia
Math312 Fall 2013
HW02 Solution and Grading Guideline
A1 (30 points 1 point each)
1. T
2. F. If Y~Bin(n,p), Y can assume 0, 1, , n, which are (n+1) possible values in total.
3. T
4. F. A counter example will be the mean for Bin(1, 0.5), where the mean (ex
Two samples problem
Hypothesis Testing on = .
, where are the corresponding sample sizes.
Reject if
100(1-)% Confidence Interval for
Matched-Pair sample problem
Paired random sample
For testing = .
Let , , =
Assumming are assymptotically normal,
, whre
Si
Mathematics 312
HW01-Math231 Review
Due: 09/05 by 4:00pm
Fall, 2013
1. Which of the following description about P-value is/are CORRECT?
(a) It is the probability for the null hypothesis bing true.
(b) The signicance level is the maximum of P-values for th
MATH/STAT 312
HW07
Fall 2013
A.1 True/False, Write down the reason if the statement you think is false.
Page 313, questions: 2,3,5,6,7,8,9,10,11,12,13,15,16,17
A.2
1. 10.1.3
2. 10.2.2
3. 10.2.4
4. 10.2.7 (Use the printout of applying SAS GLM procedure to
MATH/STAT 312
HW06
Spring 2013
A.1 True/False, Write down the reason if the statement is false.
9.1:
9.2:
9.3:
9.4:
9.5:
True, it is the definition of LSE.
False, LSE line always passes through ( , ).
True, it is the interpretation of regression coefficie
MATH/STAT 312
HW05
A.1 True/False, Write down the reason if the statement is false.
Fall 2013
8.1:
8.2:
8.3:
False, t distribution is appropriate for small sample sizes from Normal population with
unknown variance which is estimated by s2.
True.
False, un
MATH312
Fall 2013
Test I Solution Key
A (20%) Short Answer Problem. Circle the answer for True/False problem
1. (F) Given that 400 measurements of sound speed (MPH) taken in a certain lab yield the 95% C.I. for
mean sound speed, (765, 775), the probabilit
MATH/STAT 312 (Due: 11/04)
HW06
A.1 True/False, Write down the reason if the statement is false.
Fall 2013
A.2
1. (undergraduate student)Assume that X and Y are jointly distributed with E X
,E Y
, Var X
, Var Y
, Cov X, Y
. Furthermore, let Y
X
X,
.
what
MATH 312
HW03
A. True/False, Write down the reason if the statement is false.
Fall 2013
B.
5.1.9 (1) Perform manual calculation, (2) use appropriate SAS procedure to conduct the same
analysis and compare those results.)
5.2.4 (manual calculation only)
5.3
MATH 312 (Due: 10/01)
HW04
A.1 True/False, Write down the reason if the statement is false.
A.2 6.4.2
Fall 2013
B.1 True/False, Write down the reason if the statement is false.
B.2 Show all our works
1. 7.4.6
2. 7.5.4
MATH312
Spring 2013
Name:
Please circle the corresponding academic status!
Undergraduate
Graduate
Test I Feb. 18
Note :
1. You are allowed to use calculator and one page (single-sided) of formula sheet.
2. Please number extra pages if applicable.
Item
Poi
MATH/STAT 312
HW02
A.1 True/False, Write down the reason if the statement is false.
Fall 2013
A.2
B.1 True/False, Write down the reason if the statement is false.
B.2
Statistical Relation
A statistical relationship is not a deterministic (perfect) one. Observations
for a stat. relationship generally dont fall directly on the curve of
relationship, i.e. y = f (x) + where is a random error (white noise
usually).
Math312