Welcome%20to%20QM%202113-003

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Welcome to QM 2113-003
Business Statistics
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Course Objectives Again

1. To gain an understanding of descriptive
   statistics, probability, sampling, interval
   estimation, hypothesis testing, and linear
   regression.
2. To perform applications of statistical methods to
   business problems using the spreadsheet software
   Excel.

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Some statistics

• The top 3 makers of breakfast cereal account for
  95 percent of domestic sales.
• The average price of a movie ticket is 5.60.
• The dollar has lost 35 percent of its value
  against the euro since 2001.
• 20 percent of New York City students dropped out
  of school in academic year 2003-2004.
• Industrial production in China increased by 15.7
  percent in 2004.
• E-commerce sites spend an average of 108 to
  acquire a new customer.

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Statistics is the art and science of collecting,
analyzing, presenting, and interpreting data.
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Applications in Business Economics

• Accounting Auditing function, for example,
  relies on statistical sampling techniques.
• Finance Portfolio managers use a variety of
  statistics, such as the price/earnings ratio, to
  determine if shares are properly valued by the
  market.
• Marketing Market studies used for decision
  making about store or restaurant location,
  product lines or services sold, involve
  statistical analysis.

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Applications in Business Economics Continued

• Production Bottling plants use X-bar charts to
  prevent over or under fillingi.e., make sure
  that the average number of ounces falls within
  acceptable limits.
• Economics Economists use statistical techniques
  to forecast important variables such as inflation
  or unemployment.

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Elements, Variables, and Observations

• Elements are the entities on which data is
  collected.
• Variables are characteristics of interest for
  elements.
• Observations are the measurements for a
  particular element.

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Student High School Height Weight
Robert Lincoln 511 170 lbs.
Portia Southside 57 120 lbs.
Edward Oak Ridge 62 198 lbs.

• Students are the elements.
• High school, height and weight are the variables.
  
• 511, 120 lbs, etc. are the observations.

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Nominal and Ordinal Scales

• The scale of measurement for a variable is a
  nominal scale when the data are labels or names
  used to identify an attribute of the element.
• The scale of measurement is an ordinal scale if
  the order or rank of the data is meaningful.

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Student High School Height Weight
Robert Lincoln 511 170 lbs.
Portia Southside 57 120 lbs.
Edward Oak Ridge 62 198 lbs.

• The scale of measurement for the high school
  variable is nominal.
• Scales of measurement for the height and weight
  variables are ordinal.

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Scales of Measurement
Interval

• The data have the properties of ordinal data, and
• the interval between observations is expressed
  in
• terms of a fixed unit of measure.
• Interval data are always numeric.

Example Melissa has an SAT score of 1205,
while Kevin has an SAT score of 1090.
Melissa scored 115 points more than Kevin.
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Scales of Measurement
Ratio

• The data have all the properties of interval data
• and the ratio of two values is meaningful.
• This scale must contain a zero value that
  indicates
• that nothing exists for the variable at the zero
  point

Example Melissas college record shows 36
credit hours earned, while Kevins record
shows 72 credit hours earned. Kevin has
twice as many credit hours earned as Melissa.
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Qualitative and Quantitative Data

• Qualitative, or categorical, data are labels or
  names used to identify an attribute of each
  element. Can be numeric or non-numeric.
• Quantitative data are numeric values indicating
  how much or how many.

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Student High School Height Weight
Robert 1 511 170 lbs.
Portia 2 57 120 lbs.
Edward 3 62 198 lbs.

• High School remains a qualitative variableeven
  though we are now labeling it with numbers.
• Arithmetic operations for numeric qualitative
  variables are meaningless.

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Scales of Measurement
Data
Qualitative
Quantitative
Numerical
Numerical
Nonnumerical
Nominal
Ordinal
Nominal
Ordinal
Interval
Ratio
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Types of data
Time -series data historical data--i.e., the
data sample consists of a series of daily,
monthly, quarterly, or annual data for variables
such as prices, income , employment , output ,
car sales, stock market indices, exchange rates,
and so on. Cross-sectional data All observations
in the sample are taken from the same point in
time and represent different individual entities
(such as households, houses, etc.)
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Time series data Daily observations, Korean Won
per dollar
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Example of cross sectional data
Student ID Sex Age Height Weight
777672431 M 21 61 178 lbs.
231098765 M 28 511 205 lbs.
111000111 F 19 58 121 lbs.
898069845 F 22 54 98 lbs.
000341234 M 20 62 183 lbs
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Time-series graph
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Unemployment rates in industrialized countries,
May 2000
Cross-section graph
Source The Economist
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Descriptive Statistics
Summaries of data that can be in tabular,
graphical, or numerical form.
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Example Hudson Auto Repair
The manager of Hudson Auto would like to have a
better understanding of the cost of parts used in
the engine tune-ups performed in the shop. She
examines 50 customer invoices for tune-ups. The
costs of parts, rounded to the nearest dollar,
are listed on the next slide.
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Example Hudson Auto Repair

• Sample of Parts Cost for 50 Tune-ups

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Tabular Summary Frequency and Percent
Frequency
Parts Cost ()
Percent Frequency
Parts Frequency
2 13 16
7 7 5 50
4 26 32 14
14 10 100
50-59 60-69 70-79 80-89
90-99 100-109
(2/50)100
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Graphical Summary Histogram
Tune-up Parts Cost
Frequency
Parts Cost ()
50 60 70 80 90 100
110 120
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Statistical Inference
Population
- the set of all elements of interest in a
particular study
Sample
- a subset of the population
Statistical inference
- the process of using data obtained from a
sample to make estimates and test hypotheses
about the characteristics of a population
Census
- collecting data for a population
Sample survey
- collecting data for a sample
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The Process of Statistical Inference for the
Norris Electronics Example
1. Population consistsof all bulbs manufactured
with the new filament.Average lifetimeis
unknown
2. A sample of 200 bulbs ismanufactured with the
newfilament
3. The sample data provide a sample average
lifetime of 76 hours per bulb
4. The sample average is Used to estimate the
population Average.
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The Sample
Hours Until Burnout
107 85 70 60 82 89 75 89 66 91 86 94 77 61 77 65
54 78 66 80 79 63 67 77 68 77 88 93 71 62 58 58
66 90 71 67 88 74 65 72 85 63 80 77 84 85 88 76
62 81 64 83 74 85 99 81 83 68 77 77 93 59 74 71
74 62 96 94 79 65 77 64 74 71 89 78 89 61 83 86
92 70 77 89 78 84 76 57 73 79 62 72 68 82 92 92
75 66 87 76 88 66 96 98 73 65 83 81 59 79 59 45
65 78 72 84 71 59 73 98 73 73 81 87 64 72 68 75
81 75 76 68 71 74 71 86 65 88 94 84 94 68 61 102
83 86 79 64 61 85 92 69 62 62 101 92 62 70 82 76
78 72 63 68 72 75 98 81 116 75 76 66 61 84 59 65
90 67 97 103 63 69 79 70 67 79 89 63 78 62 51 73
96 68 70 71 43 82 65 63                
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Statistical Analysis Using Microsoft Excel

1. Enter the data in the Excel Spreadsheet
2. Enter functions and formulas
3. Apply tools