Imagine a researcher is interested in examining the psychological impact of principals perceived
conflict-management style on teachers productivity. In this case, the researcher is interested in
the relationships among teachers self-esteem, how teachers p
Table 4 Critical Values of Standard Normal Distribution
The entries in this table are the critical values for z for-which the area
under the curve representing a is in the right-hand tail. Critical values
for the left-hand tail are found by symmetry.
m .
MAT132 Intro to Stats
Discrete Random Variables
Kre S. Gjaldbk
Various Problems
Problem 1. Determine which of the
It is not a probability function.
functions below are probability func-
(iii)
tions.
(i)
P (x) =
(ii)
Q(x) =
(iii)
R(x) =
(iv)
T (x) =
(v)
x
MAT132 Intro to Stats
Problem 1.
Solution.
a. Let
S
Let
Homework 5
Kre S. Gjaldbk
Johnson/Kuby, p. 148, prob. 7.2.
P = cfw_1, 3, 5, 7, 9.
be the set of all samples from
P
of size 2. We then have
S = cfw_(1, 1), (1, 3), (1, 5), (1, 7), (1, 9),
(3, 1), (3,
MAT132 Intro to Stats
Basic Probability Solutions
Kre S. Gjaldbk
Basic Probability Solutions
Problem 1 (Dice). Rolling one die,
For part (v),
what is the probability of
(vii),
the sample
space consists of 36 ordered pairs,
conveniently captured by the sum
MAT132 Intro to Stats
Statistical Inferences
Kre S. Gjaldbk
Solutions Chp. 8
Prob. 3 Solution.
(iii) We have
(iii) It's a two-tail
situation with test statistic
Prob. 4 Solution.
point est.:
x = 4.02
conf. coef.: z 2 =
z 0.01
= 2.58
2
std. err.:
n
0.44
20
MAT132
Homework #2 Solutions
Kre S. Gjaldbk
Homework #2 Solutions
Problem 1
(Solutions). The various measures of centrality are (i) We have
n = 7 elements in the Danish data set, so
P
x
10 + 3 + 18 + 6 + 12 + 10 + 35
94
x =
=
=
= 13.43
n
7
7
(ii) The dept
MAT132
Homework #1 Solutions
Kre S. Gjaldbk
Homework #1 Solutions
Problem 1.
(1) We nd the relative frequency of American Football by the formula
9/51 100% = 17.65%
The rest similarly.
Sport
Rel. Freq.
American Football
17.65%
3.92%
Badminton
Basketball
9
MAT132 Intro to Stats, Kre S. Gjaldbk
Finals Review Problems
Finals Review Problems
Problem 1. In order to estimate the general
(i) The length of an
U.S. population's fondness of bow ties, an an-
elephant's trunk.
alyst paid for a highway billboard, which
MAT132 Intro to Stats
Problem 1. Given
(i)
(ii)
(iii)
Probability Practice Problems
= 0.32, P (B) = 0.10, P (A
P (A)
and
B) = 0.96,
nd
P (A).
P (A
or
P (B|A)
(iv) Are
Given
A
B).
and
and
P (A|B).
B
independent events?
P (C) = 0.15, P (D) = 0.12, P (E) =
MAT132 Intro to Stats
Statistical Inferences
Kre S. Gjaldbk
Problems Chp. 8
Problem 1.
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Find the values below.
(v) In part (iii), what is the smallest
sample size needed to guarantee
a max error of at most 0.05?
z(0.05)
z(0.005
MAT132 Intro to Stats
Statistical Inferences
Kre S. Gjaldbk
Chp. 9.2 - Inferences Regarding Population Proportions
So far, we have studied inferences regarding some population mean . Now,
we move to population proportion, p. E.g. questions like
What perce
MAT132 Intro to Stats
Statistical Inferences
Kre S. Gjaldbk
Problems Chp. 9.1
Problem 1.
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Find the values below.
(i) Let
t(8, 0.10)
H0 : = 12.2()
Ha : > 12.2
t(12, 0.05)
t(50, 0.99)
t 21, 0.05
2
Let n = 26, x = 13.8, s =
4.8. F
MAT132
Homework #2
Kre S. Gjaldbk
Homework Set #2
The tables below list a number of individuals' personal bests for juggling
a soccer ball. The rst are a group of my old friends from Denmark and me. The
second are friends of my Brazilian buddy Pedro. Pedr
MAT132 Intro to Stats
Discrete Random Variables
Kre S. Gjaldbk
Various Problems
Problem 1. Determine which of the
functions below are probability functions.
(i)
P (x) =
x
, for
15
(ii)
Q(x) =
1
, for
x
(iii)
R(x) =
x2 +3
, for
26
(iv)
T (x) =
2(3x)
, for
MAT132 Intro to Stats
Practice Exam
In order to estimate the general U.S. population's fondness of bow ties, an analyst
paid for a highway billboard, which had a picture of a handsome fellow wearing a bow tie,
accompanied by the text
Problem 1.
How Cool A
MAT132 Intro to Stats
Basic Probability
Kre S. Gjaldbk
Basic Probability Stu
Remember the
, S , is the set of all possible outcomes equally
is any subset of the sample space. The probability
sample space
. An event
of event A S is given by
likely to happe
MAT132 Intro to Stats
Linear Regression Problems
5 people were asked how many cats they own, and how many
emo songs they have on their phone. The data collected is presented in the
following table:
Problem 1.
x, cats
2 5 3 4 1
y , emo songs 15 42 27 26 9
MAT132
Homework #1
Kre S. Gjaldbk
Homework Set #1
Problem 1. Inspired by the Super Bowl, I set out to determine what the most popular sports in
the world are. In order to do this, I changed my facebook status to
Hi friends, Im doing a statistical survey.
Group Statistics
Therapy
Depression
N
Mean
Std. Deviation
Std. Error Mean
1.00
15
56.0000
9.41883
2.43193
2.00
15
45.0000
7.63451
1.97122
Independent Samples Test
Levene's Test for
Equality of Variances
t-test for Equality of Means
95% Confidence
F
Depres
Correlations
Correlations
Emission Million
GDP Trillion of $
GDP Trillion of $
Pearson Correlation
of Metric tons
1
Sig. (2-tailed)
N
Emission Million of Metric tons
Pearson Correlation
Sig. (2-tailed)
N
.882*
.001
10
10
*
1
.882
.001(P-Value)
10
10
*. Co
Q-1)
a. Mean, Median and Mode
Statistics
Credit
N
Valid
15
Missing 0
Mean
17.4000
Median
18.0000
Mode
18.00
The above table show that the credit hours taken during the final term of senior year has a mean
of 17.4, a media of 18, and a mode with equal to t
EXERCISE I
(A & B)
Frequencies
Statistics
Movies
N
Valid
25
25
0
0
1.4800
1.0000
1.12250
.00000
Missing
Mean
Std. Deviation
Frequency
The Sample has a mean of 1.48 and a standard deviation of 1.12
Frequency Table
Movies
Cumulative
Frequency
Valid
Percent
Material zur der Prfung im Fach Biologie
1)
Empfohlene Literatur
Duden: Basiswissen Schule, Biologie-Abitur, Duden-Verlag
Linder: Biologie, Schroedel-Verlag
Natura: Biologie fr Gymnasien, 3b NRW, Klett-Verlag
2)
Struktur der Klausur
Die Dauer der Klausur
NOTE to prospective students: This syllabus is intended to provide students
who are considering taking this course an idea of what they will be learning. A
more detailed syllabus will be available on the course site for enrolled students
and may be more c
Mathematics IA
Worked Examples
ALGEBRA: THE VECTOR SPACE Rn
Produced by the Maths Learning Centre,
The University of Adelaide.
May 1, 2013
The questions on this page have worked solutions and links to videos on
the following pages. Click on the link with
MATH 423
Linear Algebra II
Lecture 8:
Subspaces and linear transformations.
Basis and coordinates.
Matrix of a linear transformation.
Linear transformation
Denition. Given vector spaces V1 and V2 over a
eld F, a mapping L : V1 V2 is linear if
L(x + y) = L