PERM UTATIONS AND COM BINATIONS
Factorial and Basic Counting Principles
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2. Multiplication Pmciple of Counting - A fundamental way to count the amber
always something cauhappen
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L Factorial-the product orpositive imam S 12:03 2
gm Evaluate the
Introduction to Statistics
Historical Notes
The earliest statistical recordings include:
Ancient Babylonians recorded their crop yields on clay tablets.
Ancient Egyptian pharaohs recorded their wealth on stone walls.
History of Statistics
1663 Scholars pi
The group conducted a mercantile survey to know if students are willing to invest
their money in stocks or they will use the money to open up a business. This survey
also shows:
1. The reasons why students want to invest their money in stocks.
2. If the s
CPROBS2 Reviewer
CH1 INTRODUCTION
Production Creation of goods & services
Operations Management Set of activities
that create value in the form of goods and
services by transforming inputs into outputs
ESSENTIAL FUNCTIONS
1. Marketing Generates demand
2.
Derivatives - Tutorial #6 Solutions
1. See notes
Questions
2. 18-1 The market value of an option is typically higher than its exercise
value due to the speculative nature of the investment.
Options allow
investors to gain a high degree of personal leverag
GROUP7
Chapter 12 Rapid Review
Managing Inventory
Inventory is one of the most expensive asset of many companies.
The objective of inventory management is to strike a balance between inventory
investment and customer service.
2 basic Inventory issues are
Statistical hypothesis
tests on multiple
populations
The tests discussed so far deal with
assessing one population parameter or
comparing two population parameters
What if there are more than two
populations?
For instance, what if there are four populatio
IV. Data analysis and interpretation
Point Estimation
Interval Estimation
Incorporating probability into sample
values allows a researcher to not just
describe the sample but also infer about
the population
This is called inferential statistics
Estimation
Step 2: Data
Collection (Part 2
of 3)
After sampling, the researcher must reach
the sample units and gather data from them
There are many different ways of doing so
Some data gathering
methods
1. Survey
2. Observation
3. Content Analysis
4. Experiment
5.
Point and Interval
Estimation for Two
Population
Parameters
-Angelo Alberto-
Part 1 deals with estimation of
parameters for one population
Sometimes, a researcher needs to
estimate parameters for the difference
between two populations
A random sample o
DETERMINING THE
TAIL OF THE TEST:
EXAMPLES FROM OWN
STUDIES
Alberto and Kwan (2009) aimed to determine if high
school students who seldom use audiovisual media
(TV, Internet) read more than students who
frequently use audiovisual media.
Upper tail test
:
W
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4
STEP
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ANGELO ALBERT
GOALS
REDUCE LARGE AMOUNTS OF DATA INTO A FEW VALUES
THAT BEST REPRESENT THE DATA
REVEAL MEANINGS BEHIND THE DATA
DESCRIBE THE SAMPLE IN DETAIL
PREDICT PROBA
Step 2: Data
Collection
(Part 1 of 3)
Angelo Alberto
In statistics, data may be classified
according to source
Primary data
Secondary data
Primary data
Data coming from the researcher
himself/herself
The researcher is the one conducting the
actual st
STATISTICAL HYPOTHESIS
TESTS ON TWO POPULATIONS
One population tests deal with testing
assumptions on one population parameter
only
Sometimes, a researcher needs to test an
assumption on the difference between two
population parameters
EXAMPLE 1
A random
Data Analysis and
Interpretation
- Part 2: Tables and
Graphs
I. Some examples of tables
Mea
n
SD
Number of household appliances
4.7
0.3
Number of employed household
members
2.9
0.1
Age of household head
49.3
14.1
Estimated monthly internet
expenditure
503
IV. Data Analysis and Interpretation (Part 3)
Probability
Inference from sample to population requires
principles of certainty and uncertainty
Decisions based on a sample but linked to the
population must be guided by the likelihood of
events occurring
Step 1: Planning a
study
Angelo Alberto
Research problem/s
The main question/s that the research
attempts to answer
Should actually be answered by the end of
the research
Research objectives
Steps performed to fully answer the
research problem/s
Probl
STATISTICS: AN OVERVIEW
ANGELO M. ALBERTO, MOS
STATISTICS IS THE SCIENCE AND ART OF PLANNING A
RESEARCH STUDY, COLLECTING DATA FOR THE
STUDY, ENCODING/PROCESSING THE DATA
COLLECTED, ANALYZING AND INTERPRETING
ENCODED DATA, AND PRESENTING FINDINGS OF THE
S
DATA COLLECTION
(PART 3 OF 3)
LEVELS OF MEASUREMENT OF VARIABLES
Knowing the level of measurement of a
variable helps in encoding, analyzing,
interpreting and presenting the values of
this variable
FOUR LEVELS OF
MEASUREMENT
1)
2)
3)
4)
Nominal
Ordina
Regression analysis
(Part 1)
Dependent variable (Y)
Independent variable (X)
Greene and Touchstone conducted a study
to relate birthweight and estriol level in
pregnant women. Following are their sample
data
Estriol
(mg/ 24 Birthweigh
hr)
t (g/100)
7
25
9
Principles of
sampling distribution
Recall from previous ppt files:
Probability distribution
Distribution
of probabilities over all possible
values of a discrete or a continuous random
variable
Sampling distribution
Distribution
of probabilities over al
Statistical hypothesis tests on
multiple populations (Part 4)
So far
One
population
Two
populations
More than
two
populations
Means
Z test or t
test
Z test or t
test
Proportions
Z test
ANOVA with
post-hoc test
?
Z test
Chi square goodness-of-fit
(GoF) tes
IV. Data Analysis and
Interpretation (Part
3)
- Continuous
Probability
distributions
Continuous random variable
A random variable for which the values are defined within a
range
Literally any value within the range may be a value of a
continuous RV
The va
Statistical hypothesis
tests on multiple
populations
(PART 2)
RECALL: Example 1
Consider the following data on the number of hours of
pain relief provided by 5 different brands of headache
tablets (A, B, C, D, E) administered to 25 subjects
A
5
4
8
6
3
B
Two-way ANOVA
The previous examples deal with observations
grouped according to one factor or grouping variable.
In practice, there can be two factors
Such situation is addressed by Two-Way ANOVA
In Two-Way ANOVA, the objective is to know whether the
vari
Step 4:
Data Analysis and
Interpretation (Part 1)
Angelo Alberto
Descriptive statistics
Inferential statistics
Parameter
Value of the parameter comes from the population
Statistic
Value of the statistic comes from the sample
Ungrouped data
Grouped
IV. Data Analysis and
Interpretation (Part 3)
Random variables
Discrete Probability
distributions
Random variable
Random variable (RV)
A function that assigns numeric values to
different events in a sample space
TWO TYPES:
Discrete random variable
Con