The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2014
MATH2411 Applied Statistics
Tutorial Notes 7
Data Analysis
Math Support Centre
Example 1 (Box Plot)
In 201314 Fall Semester, there were 22 students in MATH2411 Tutorial T1A. The
Midterm score of these 22 students are listed below:
Wednesday 127pm@2612
(
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
Tutorial note of Math 144
8/Feb, 2010
1.A tire manufacturer wants to determine the inner diameter of
certain grade of tire. Ideally, the diameter would be 570 mm. The
data are as follows:
572 572 573 568 569 575 565 570 750
(a). Find the sample mean, medi
The Hong Kong University of Science and Technology
applied statistics
MATH 2411

Fall 2014
Chapter Three
1. Random Variables and
Probability Distributions
1
Random Variables
2
Consider an experiment of randomly selecting three cards
from a deck of 52 cards without replacement. Denote A as
an ace card and N as a nonace card. Then
S = cfw_ AAA ,
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
MATH2411: Applied Statistics (Estimation)
1. For a chisquare distribution nd the following:
a) 2 0.005 when = 5; b) 2 0.05 when = 19;
,
,
c) 2 0.01 when = 12.
,
2. For a chisquare distribution nd 2 such that
,
a) P (U > 2 ) = 0.99 when = 4;
,
b) P (U >
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
MATH2411: Applied Statistics  Dr. YU, Chi Wai
Chapter 3: RANDOM VARIABLES (contd)
6
WELLKNOWN DISTRIBUTIONS
The following wellknown distributions are important in statistics as many results
are derived for them leading to quick analyses.
Discrete Dist
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
MATH2411: Applied Statistics  Dr. YU, Chi Wai
Chapter 3: RANDOM VARIABLES
1 WHAT IS A RANDOM VARIABLE?
In chapter 2, we defined an event which is a subset/portion of outcomes from the
sample space that we are interested. Indeed most often we are more int
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
MATH2411: Applied Statistics  Dr. YU, Chi Wai
Chapter 5: HYPOTHESIS TESTING
1 WHAT IS HYPOTHESIS TESTING?
As its name indicates, it is about a test of hypothesis. To be more precise, we
would translate our question of interest into a hypothesis about a p
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
MATH2411: Applied Statistics  Dr. YU, Chi Wai
Review Questions for Chapter 6: Simple linear regression
1.
The following table contains the data of a response variable and two explanatory variables and :
2.48
2.26
2.47
2.77
2.99
3.05
3.18
3.46
3.03
3.26
2
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
MATH2411: Applied Statistics  Dr. YU, Chi Wai
Review Questions for Chapter 5: Hypothesis Testing
1. The following are the weights, in decagrams, of 10 packages of grass seed distributed
by a certain company:
46.4, 46.1, 45.8, 47.0, 46.1, 45.9, 45.8, 46.9
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
MATH2411: Applied Statistics  Dr. YU, Chi Wai
Review Questions for Chapter 3: Random variables
(contd)
1. The probability that a brand of notebook computer will survive a shock test
is . Find the probability that
a. only 2 of the next 4 computers tested
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
MATH2411: Applied Statistics  Dr. YU, Chi Wai
Review Questions for Chapter 3: Random variables
1. Consider the return per $1000 for two type of investments
P(X) and
P(Y)
0.2
0.5
0.3
Dow Jones
Funds (X)
$100
$100
$250
Government
Bond (Y)
$200
$50
$100
C
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
MATH2411: Applied Statistics  Dr. YU, Chi Wai
Review Questions for Chapter 4: Estimation
1. The following are the weights, in decagrams, of 10 packages of grass seed distributed
by a certain company:
46.4, 46.1, 45.8, 47.0, 46.1, 45.9, 45.8, 46.9, 45.2,
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
(do 0w
MATH2411 Applied Statistics Tutorial Notes 7
Examples
Example 1
A random sample of 64 bags of White Cheddar Popcorn weighed, on average, 5.23
ounces with a population standard deviation of 0.24 ounces. Test the hypothesis that
[1. = 5.5 ounces agai
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
sat/9%“
MATH2411 Applied Statistics Tutorial Notes 8 (c) evaluate .92. I Z 1 (Q 7‘“ 21 lg g: (6.51, ‘
Examples g'mcsb 9791.: i (9“: "5(4) : ‘1" ‘ n :1 ' \E‘r S) l
 " " _ k I) '0‘ log. ‘
Example 1 €13 a ‘3 Cir“‘l‘ja'fj’ 1 i ‘13. WﬂSLﬂ—fiE—llﬁ
A study w
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
MATH2411: Applied Statistics  Dr. YU, Chi Wai
Review Questions for Chapter 7: GOF
1.
Test if the data shown on the following table are from a Poisson distribution with
mean = 0.4 at a significance level 0.05.
Value
Observed
frequency
2.
0
65
1
25
2
8
3
2
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
MATH2411: Applied Statistics  Dr. YU, Chi Wai
Chapter 2: PROBABILITY
1 WHAT IS PROBABILITY?
Probability is the study of randomness. A probability of an uncertain outcome/event is the
chance (or likelihood) that it will occur.
The probability must be betw
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
Chapter 8
ANOVA models
1
1. ANOVA models
In Chapter 5 (Hypothesis Testing), we are restricted in testing for the mean of
ONE random variable from a normal distribution.
Here we would add one or more normal random variable, and then test the
equality of th
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
MATH2411: Applied Statistics  Dr. YU, Chi Wai
Chapter 1: DESCRIPTIVE STATISTICS
1 WHAT ARE DATA?
Data (its singular form is datum) in science are a collection of measurements and identifiers.
These can take many forms like numerical, character, or any ot
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
MATH2411: Applied Statistics  Dr. YU, Chi Wai
Review Questions for Chapter 2: Probability
1. Show that
( )) = () + () ( )).
2. Draw a Venn diagram for ().
3. A mother has two kids. Find the probability that they are both boys if
a. You ask the mother
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
MATH2411: Applied Statistics  Dr. YU, Chi Wai
Chapter 7: GOODNESS OF FIT TEST
1 WHAT IS A GOODNESS OF FIT (GOF) TEST?
Goodness of Fit test is one special hypothesis test to determine whether or not
our collected data (or equivalently, X) are from a hypot
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
MATH2411: Applied Statistics  Dr. YU, Chi Wai
Chapter 0: Introduction to Statistics
1 WHAT IS STATISTICS?
Statistics is .
a mathematical science that pertains to the data collection, data analysis,
data interpretation, data explanation and data presenta
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
MATH2411: Applied Statistics  Dr. YU, Chi Wai
Chapter 4: ESTIMATION
1 ESTIMATION (STATISTICAL METHODOLOGY)
In chapter 3, we defined a random variable X and had a new interpretation of
data  the actual values of the random variable. Recall that if the di
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
MATH2411: Applied Statistics  Dr. YU, Chi Wai
Review Questions for Chapter 1: Descriptive
statistics
1. A manufacturer of insulation randomly selects 20 winter
days and records the following daily high temperature:
24, 35, 17, 21, 24, 37, 26, 46, 58, 30,
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
MATH2411: Applied Statistics  Dr. YU, Chi Wai
Chapter 6: SIMPLE LINEAR REGRESSION
1 WHAT IS A SIMPLE LINEAR REGRESSION?
Regression is a very useful statistical model used to capture a relationship
between related variables of our interest. If the relatio
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
Solutions for Hypothesis Testing
1.
Test H0 : X = 800 vs H1 : X = 800 at a level of 0.05.
Note that 788800 = 1.64 < z0.025 = 1.96. So, we do not reject H0 at a level of 0.05. The mean of the
40/ 30
lifetime is NOT signicantly dierent from 800.
2.
Test H0
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
MATH2411: Applied Statistics (Hypothesis Testing)
1. An electrical rm manufactures light bulbs that have a lifetime that is normally distributed with a
standard deviation of 40 hours. Test the hypothesis that X = 800 hours against the alternative
X = 800
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
r' j a 
, a LA . . . . .
MATH2411 Applied Statistics 3 K 0 A Tutorial Notes 6 Example 2 (Chisquare Distribution)
For a chisquared distribution ﬁnd xﬁ such that
, (a) P(X2 > xi) = 0.99 when u : 4;
Example 1 (Student’s tDistribution)
(a) Find P(T < 2.36
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
MATH2411 Applied Statistics “E’CK'VVJFTC V\ Tutorial Notes 4 Example 3 (continuous PPObability DiStribUtion)
If a dealers proﬁt, in units of $50001 on a new automobile can be looked upon as a
Examples random variable X having the density function
Example
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Fall 2015
Question 1
Question 2
Question 3
Question 4
Question 5
Math 144 tutorial 5
March 15, 2010
Question 6
Question 7
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
1. Let the probability density function of a random variable X be
given by
x
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Spring 2014
HKUST
Math 2411: Applied Statistics
Midterm Examination (Spring 2012)
Name:
21th March 2012
19:0021:00
Student I.D.:
Tutorial session:
Directions:
This is a closed book examination and the exam will be
2 hours long.
Write down your FULL name, student ID
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Spring 2014
Probabilities
2.1
Fundamental Formulation of Probabilities
Definition 2.1 A sample space is the set of all possible outcomes of an experiment/observation. A subset of such a sample space is called an event.
Example 2.2 A coin is tossed in an experiment. T
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Spring 2014
Set Notation
1.1
Sets Operations
Definition 1.1 A set is a collection of objects.
Definition 1.2 If A is a set and x is an object so that x belongs to A, we write
x A.
Definition 1.3 A set A is a subset of another set B if for every x A, x B.
In this circ
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Spring 2014
HKUST
Math 2411: Applied Statistics
Final Examination (Spring 2012)
Name:
17th May 2012
8:3010:30
Student I.D.:
Seat number:
Directions:
This is a closed book examination and the exam will be
2 hours long.
Write down your FULL name, student ID number, a
The Hong Kong University of Science and Technology
Applied Statistics
MATH 2411

Spring 2014
Math 2411 Applied Statistics
Fall 2016
Summary of Course Materials
Operations of Probabilities and Basic Counting Principles
HKUST
Page 1 / 9
Conditional Probability
Discrete Random Variables
Continuous Random Variables
HKUST
Page 2 / 9
Tutorial 1
Exercis