QUIZ 1: STAB57H3 - An Introduction to Statistics
FIRST NAME:
LAST NAME:
STUDENT NUMBER:
TUTORIAL:
Problem 1: The following data were generated from an N (, 1) distribution by a student.
Unfortunately, the student forgot which value of was used, so we are
5.3 Statistical Models p247
In a statistical problem, we observe data s,
but we are uncertain about P. We want to
construct inferences about P.
We assume that there is a random
mechanism generating s and we know that
the corresponding probability measure
R code for example 9.1.2 p482
#Example 9.1.2 p482
n = 5 # sample size in this example
rep=100000
d=c(1:rep) # just define an arbitrary initial vector
for(i in 1:rep) cfw_
s=rnorm(n,mean=0,sd=1)
#print(s)
r=(s-mean(s)/sd(s)
#print(r)
d1=log(r^2)/(n-1)
d[i]
UNIVERSITY OF TORONTO AT SCARBOROUGH
UNIVERSITY OF TORONTO AT SCARBOROUGH
SAMPLE FINAL EXAM
STAB57
Duration - 3 hours
THIS EXAM IS OPEN BOOK (NOTES)
AIDS ALLOWED: Non-communicating calculator
LAST NAME_
FIRST NAME_
STUDENT NUMBER_
All relevant work MUST b
STAB57H3 Midterm Test
Midterm Test
March, 2010
Duration: one hour and fifty minutes
Please do NOT open this booklet until you are asked to do so
There are 9 pages including this page. Please check to see if you have all the pages.
Aids allowed: This test
Ex.
Degree of Reading Power (DRP) scores
for 44 students. Assume that the
population standard deviation is 11.0.
95% CI for the population mean score
is given in the MINITAB output below.
DRP Scores
40
19
31
49
27
26
47
46
28
14
39
19
52
52
54
14
26
25
47
10.3.2 Simple linear regression
In simple linear regression we assume
E(Y | X = x) = + x
12
Estimation of parameters
Given n observations on the explanatory variable x
the response variable y,
( x , y ),( x , y ),( xn, yn )
11 2 2
b is estimated by
2
n
n
Chi-squared test for independence of
two categorical variables
Table <- matrix(c(24,9,13,289, 100, 565), 2, 3, byrow=TRUE)
rownames(Table) <- c('Flu', 'No Flu')
colnames(Table) <- c('No Vac', 'One shot', 'Two shots')
Table
chisq.test(Table)
Here is the R
STAB57: Quiz-10 Solutions
[All relevant work must be shown for full credit]
Name:
Student number:
Suppose that we have observed a sample: x1 , x20 from a N (, 22 ) and found that x =
5.567 and s = 2.05. Let 21 be another independent observation from the s
gmacro
SampleSizeTConfInt
#This is a MINITAB macro calculates the sample size for t CIs for the difference
#between two population means. See p321 Evans and Rosenthal for details.
#To run this macro just save it in some folder and open minitab
#and at th
t Table
cum. prob
t .50
t .75
t .80
t .85
t .90
t .95
t .975
t .99
t .995
t .999
t .9995
one-tail
0.50
1.00
0.25
0.50
0.20
0.40
0.15
0.30
0.10
0.20
0.05
0.10
0.025
0.05
0.01
0.02
0.005
0.01
0.001
0.002
0.0005
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.00
STAB57: Quiz-1
[All relevant work must be shown for full credit]
Name:
Student number:
1) A random variables X has a continuous distribution for which the p.d.f. is as follows:
=
4,
0,
0<
<1
a) [4 points] Determine the prediction of for a future X, if we
STAB57: Quiz-1 Tutorial 1
(Show your work clearly)
Last Name:
Student number:
First Name:
1. random variable X has a continuous distribution for which the p.d.f. is as follows:
f ( x) =
k x2.5
0
0<x<1
otherwise
where k > 0 is a constant.
(a) (4 points) De
UNIVERSITY OF TORONTO AT SCARBOROUGH
STAB57H3
Winter 2014
An Introduction to Statistics
Course Description: STAB57H3 introduces the basics of statistical methodology and
the theories that justify the way we conduct statistical analyses. It builds on the m
UNIVERSITY OF TORONTO SCARBOROUGH
Department of Computer and Mathematical Sciences
Midterm Test, February 2014
STAB57H3 Introduction to Statistics
Duration: One hour and fty minutes
Last Name:
First Name:
Student number:
Aids allowed:
- The textbook (Prob
UNIVERSITY OF TORONTO SCARBOROUGH
Department of Computer and Mathematical Sciences
Midterm Test, March 2012
STAB57H3 Introduction to Statistics
Duration: One hour and fty minutes
First Name:
Last Name:
Student number:
Aids allowed:
- The textbook (Probabi
Optimization in R.
Ex1 Find ArgMin (f, x) where
f ( x) = x2 3x + 2
f <- function(x) x^2-3*x+2
optimize(L, interval = c(0, 3)
# Note an interval is required.
$minimum
[1] 1.5
$objective
[1] -0.25
>
1
Ex 2 The coin tossing example we discussed in
class. Tos
UNIVERSITY OF TORONTO SCARBOROUGH
Department of Computer and Mathematical Sciences
FINAL EXAMINATION, APRIL 2012
STAB57H3 Introduction to Statistics
Duration: 3 hours
First Name:
Last Name:
Student number:
Aids allowed:
- The textbook (Probability and Sta
10.3.2 Simple linear regression p540
In simple linear regression we assume
E(Y | X x) x
12
Estimation of parameters
Given n observations on the explanatory variable x
the response variable y,
(x , y ),(x , y ),(xn, yn)
11 2 2
b is estimated by
2
n
n
( xi
QUIZ 6: STAB57H3 - An Introduction to Statistics
FIRST NAME:
LAST NAME:
STUDENT NUMBER:
TUTORIAL:
Problem 1: Let (x1 , x2 , , xn ) be a random sample from an Exponential() distribution. Consider that the prior distribution of is Gamma(0 , 0 ). Find the di
QUIZ 7: STAB57H3 - An Introduction to Statistics
FIRST NAME:
LAST NAME:
STUDENT NUMBER:
TUTORIAL:
Problem 1: The concentration of mercury (milligrams per cubic meter) is a random variable
(say X) having a N (, 0.52 ) where N (1.5, 0.72 ). A sample of 11 m
QUIZ 9: STAB57H3 - An Introduction to Statistics
FIRST NAME:
LAST NAME:
STUDENT NUMBER:
TUTORIAL:
Problem 1: The director of admissions of a small college selected 5 students at random
from the new freshman class in a study to determine whether a students
QUIZ 8: STAB57H3 - An Introduction to Statistics
FIRST NAME:
LAST NAME:
STUDENT NUMBER:
TUTORIAL:
2
Problem 1: Let (X1 , X2 , , Xn ) be a random sample from an N (, 0 ), where R1 is
2
unknown and 0 is known. Dene the ith residuals as
Ri = Xi X.
Prove that
QUIZ 10: STAB57H3 - An Introduction to Statistics
FIRST NAME:
LAST NAME:
STUDENT NUMBER:
TUTORIAL:
Problem 1: Suppose that a census is conducted on a population and the joint distribution
of (X, Y ) is obtained as in the following table.
Y =1 Y =2 Y =3
X=
QUIZ 10: STAB57H3 - An Introduction to Statistics
FIRST NAME:
LAST NAME:
STUDENT NUMBER:
TUTORIAL:
Problem 1: In a certain Federal Power Commission hearing some years ago, witnesses
presented the following data (here rounded). The variables are: (i) predi
UNIVERSITY OF TORONTO SCARBOROUGH
Department of Computer and Mathematical Sciences
FINAL EXAMINATION, APRIL 2013
STAB57H3 Introduction to Statistics
Duration: 3 hours
First Name:
Last Name:
Student number:
Aids allowed:
- The textbook (Probability and Sta