The Hong Kong University of Science and Technology
BUSINESS STATISTICS
BUSINESS 2500

Fall 2014
ISOM 2500 Answer 2
Problem 1
Match the description to the scatterplot.
(a) No pattern. A plot of scrambled pairs would look the same.
(b) Negative direction, linear, small variation around line.
(c) Positive direction, but bending with small variation aro
The Hong Kong University of Science and Technology
statistic
BUSINESS 2500

Fall 2014
Hypothesis Testing for mean 12
when s are known
H0: 12 =d
Normal populations
z
or large sample size,
Observed test statistic
( x1 x2 ) d
12
n1
2
2
n2
Z
Z
Z
88
The Hong Kong University of Science and Technology
statistic
BUSINESS 2500

Fall 2014
Example The Valentines Day Chocolate Box
Candy company have designed a new box
Last years mean order quantity of large retail
stores was 330 boxes. The company needs to
assess whether it is reasonable to plan for the
same boxes this year.
The null hypothe
The Hong Kong University of Science and Technology
statistic
BUSINESS 2500

Fall 2014
Example  Payment Time
With new billing system, the mean bill paying
time is hoped to be less than 19.5 days
With old billing system, the mean bill paying
time was close to but not less than 39 days
Alternative hypothesis Ha is the new billing system
has
The Hong Kong University of Science and Technology
statistic
BUSINESS 2500

Fall 2014
How do you test them?
Hiring System  whether or not the individual
predicts to be a good employee.
The training course is useful for improving
productivity
The boss of the firm hope that its useful
The employee dont want to take extra course
Stock prices
The Hong Kong University of Science and Technology
statistic
BUSINESS 2500

Fall 2014
Example  Trash Bag
H0: 50
x 50 x 50
With 0 = 50, use
z
x
n
the test statistic:
If z 0, then x 0 and there is no evidence
to support rejecting H0 in favor of Ha
versus Ha: > 50
The point estimate x indicates is probably less than
50
If z > 0, then x > 0
The Hong Kong University of Science and Technology
statistic
BUSINESS 2500

Fall 2014
Errors in Making Decisions
Type I Error
Reject True Null Hypothesis
Has Serious Consequences
Probability of Type I Error Is
Called
Level of Significance / Significance level
Set by researcher, or by the users in advance
Type II Error
Do Not Reject
The Hong Kong University of Science and Technology
statistic
BUSINESS 2500

Fall 2014
How to choose between &
Choice depends on the cost of the error
Choose little when the cost of rejecting the H0 is
high
The oil tank making: Causing an oil tanker to sink
H0 : the tank is defective
=P( the tank meet the standard  the tank is defective)
The Hong Kong University of Science and Technology
statistic
BUSINESS 2500

Fall 2014
Factors Affecting
True Value of Population Parameter
Increases When Difference Between Hypothesized
Parameter & True Value Decreases
Significance Level
Population Standard Deviation
Increases When Decreases
Increases When Increases
Sample Size n
Incre
The Hong Kong University of Science and Technology
statistic
BUSINESS 2500

Fall 2014
Exercise Managers Promotion
Suppose the company AA's monitor team periodically
conducts spot checks to determine whether the mean
lifetime of the new torch is exceeds 1,200 hours during the
testing period, if it is, then the company will launch these
new
The Hong Kong University of Science and Technology
statistic
BUSINESS 2500

Fall 2014
Hypothesis Testing Process
Assume the
population
mean age is 50.
(Null Hypothesis)
Is x 20 50?
No, not likely!
Population
The Sample
Mean Is 20
REJECT
Null Hypothesis
Sample
4
The Hong Kong University of Science and Technology
statistic
BUSINESS 2500

Fall 2014
Types of Hypotheses
OneSided, Greater Than Alternative
H0: 0 vs. Ha: > 0
OneSided, Less Than Alternative
H0 : 0 vs. Ha : < 0
TwoSided, Not Equal To Alternative
vs. Ha : 0
H0 : = 0
where 0 is a given constant value.
13
The Hong Kong University of Science and Technology
statistic
BUSINESS 2500

Fall 2014
Types of Decisions
As a result of testing H0 vs. Ha, will have
to decide either of the following decisions
for the null hypothesis H0:
Do not reject H0
A weaker statement than accepting H0
Reject H0
<=> accepting Ha
14
The Hong Kong University of Science and Technology
statistic
BUSINESS 2500

Fall 2014
Hypothesis Testing for mean 12
when s are unknown
H0: 12 =d
Test Statistic
1 =2,
normal population
( X1 X 2 ) d
~ t n1 n2 2
t
1
2 1
Sp( )
n1 n2
1 =2,
normal population,
n1+n22>=30
( X1 X 2 ) d
Z
~ N (0,1)
1
2 1
Sp( )
n1 n2
no information about
populati
The Hong Kong University of Science and Technology
statistic
BUSINESS 2500

Fall 2014
Example
HK government claims that the average monthly
salary in 2006 is $4500 more than Macaus. We
want to test the governments claim.
We take a sample of HK (n1=1000) and a
sample of Macau (n2=1000) , the sample means
are $8500 for HK and $6500 for Macau
The Hong Kong University of Science and Technology
statistic
BUSINESS 2500

Fall 2014
What is a Hypothesis?
A hypothesis is an
assumption about the
population parameter.
A parameter is a
characteristic of the
population, like its mean
or variance.
I assume the mean GPA
of this class is 3.5!
The parameter must be
identified before analysis.
The Hong Kong University of Science and Technology
statistic
BUSINESS 2500

Fall 2014
What is Hypothesis Testing?
The intent of hypothesis testing is formally examine two
opposing conjectures (hypotheses), H0 and HA.
These two hypotheses are mutually exclusive and
collectively exhaustive so that one is true to the exclusion of
the other.