Problem Set 2
Due: February 10, 2017 by 12pm (or in class during week 26)
1. A company is selling radio sets. Historical records over the past 100 weeks
show 6 weeks with no radios sold, 30 weeks with 1 radio sold, 30 weeks
with 2 radios sold, 20 weeks wi
Classroom discussion 1
To be discussed on 3rd week
1. In the US the salaries of superstar professional athletes receive much attention in the
media. The multi-million dollar long-term contract is now commonplace among this
elite group. Nevertheless, rarel
STAT101
INTRODUCTORY
STATISTICS
Who am I
Dr. Lin Ting Kwong
Senior Lecturer of Statistics
School of Economics
Research interest in Survey Sampling
SOE 05-045
Email address: [email protected]
Consultation Hours
Wednesday and Thursday
10.30 am to 11.30 am
SO
Classroom discussion 6
On 10th week
1. In leaving for school on an overcast April morning you make a judgment
on following null hypothesis. H 0 : The weather will remain dry.
What would be results be of Type I and Type II errors?
A. Type I error: get dren
Hypothesis Test
Basic Concepts
1
Relationship between Type I
error and Type II error
2
Example :
The manager of a department store is thinking about
establishing a new billing system for the store' s credit
customers. After a thorough financial analysis,
United Airlines Flight Arrivals at Chicago O'Hare (n = 278 flights)
Data are for Tuesday, April 26. 2005.
Data are for Tuesday, April 26. 2005.
Source: http:/www.bts.gov
Source: http:/www.bts.gov
Obs
Flight Number
Tail Number
Origin Airport
Scheduled
Arri
Continuous Probability
Distributions
Continuous Probability
Distributions
A continuous random variable is a variable that can
assume any value on a continuum (can assume an
uncountable number of values)
thickness of an item
time required to complete a ta
Hypothesis Test
Paired Samples
1
In this section, a procedure is developed for
analyzing the difference between the means
of two groups when the sampled data are
obtained from populations that are related :
when the results of the first group are not
ind
1
Hypotheses Test
One sample
2
Estimation vs Hypothesis tests
In estimation we answer to the question
what? (the amount of the event)
For example, what proportion of the
population will visit the integrated resort?
In hypothesis test we answer to the qu
Discrete Probability Distribution
Random Variables
Definitions
Random Variables
A random variable represents a possible
numerical value from an uncertain event.
Discrete random variables produce outcomes
that come from a counting process (i.e.
number of
Estimation
Estimator and statistic is interchangeble
Point Estimation
An important use of data obtained from a
sample is to be able to draw inference about
certain characteristics of the population, such
as the mean, the variance and the proportion of
th
Hypothesis Test
Paired Samples
1
In this section, a procedure is developed for
analyzing the difference between the means
of two groups when the sampled data are
obtained from populations that are related :
when the results of the first group are not
ind
1
x x
n
s
2
x x
2
n1
1
x2
n 1
2
x
n
2
E X xp x
COV ( X , Y ) xyp x, y x y
V(X) = 2 x E X p x
COV ( X , Y ) E ( XY ) E ( X ) E (Y )
2 E ( X 2 ) ( E[ X ]) 2
1
for k 1
k2
x can be considered an outlier if x>Q3+1.5(IQR) or x< Q1 -1.5(IQR)
P k X k 1
Hypothesis Test
Basic Concepts
1
Relationship between Type I
error and Type II error
2
Example :
The manager of a department store is thinking about
establishing a new billing system for the store' s credit
customers. After a thorough financial analysis,
Summary
Why study Statistics
We got some problems (usually it is quantifiable) in
the population we want an answer.
It is too costly, time consuming even if we have the
money, lack of manpower for us to gather all the
information of the population.
Thu
Sampling and Sampling distribution
Sampling
Why sample?
Cheaper :
n<N
n is determined by budget, time, resources and the level of
accuracy desired in the survey study.
Faster
n<N
N is determined by the nature of the problem (sampling
fraction)
e.g. Intere