Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 1-1

Winter 2006

Introduction

MS 205Quantitative Business Modeling

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.. Chap 1-2

Basic Concepts of Statistics

Statistics is concerned with:

Processing and analyzing data Collecting, presenting, and transforming

data to assist decision makers

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.. Chap 1-3

Key Definitions

A population (universe) is the collection of all members of a group

A sample is a portion of the population selected for analysis

A parameter is a numerical measure that describes a characteristic of a population

A statistic is a numerical measure that describes a characteristic of a sample

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.. Chap 1-4

Population vs. Sample

a b c d

ef gh i jk l m n

o p q rs t u v w

x y z

Population Sample

b c

g i n

o r u

y

Measures used to describe a population are called parameters

Measures computed from sample data are called statistics

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.. Chap 1-5

Two Branches of Statistics

Descriptive statistics Collecting, summarizing, and presenting data

Inferential statistics Drawing conclusions about a population based

only on sample data

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.. Chap 1-6

Descriptive Statistics

Collect data e.g., Survey

Present data e.g., Tables and graphs

Characterize data e.g., Sample mean =

iX

n

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.. Chap 1-7

Inferential Statistics

Estimation e.g., Estimate the population

mean weight using the sample mean weight

Hypothesis testing e.g., Test the claim that the

population mean weight is 120 pounds

Drawing conclusions about a population based on sample results.

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.. Chap 1-8

Collecting Data

SecondaryData Compilation

Observation

Experimentation

Print or Electronic

Survey

PrimaryData Collection

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.. Chap 1-9

Types of Data

Data

Categorical Numerical

Discrete Continuous

Examples:

Marital Status Political Party Eye Color (Defined categories) Examples:

Number of Children Defects per hour (Counted items)

Examples:

Weight Voltage (Measured characteristics)

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc..

Levels of Measurementand Measurement Scales

Interval Data

Ordinal Data

Nominal Data

Highest Level

(Strongest forms of measurement)

Higher Levels

Lowest Level

(Weakest form of measurement)

Categories (no ordering or direction)

Ordered Categories (rankings, order, or scaling)

Differences between measurements but no true zero

Ratio DataDifferences between measurements, true zero exists

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc..

Levels of Measurementand Measurement Scales

Interval Data

Ordinal Data

Nominal Data

Height, Age, Weekly Food Spending

Service quality rating, Standard & Poor’s bond rating, Student letter grades

Marital status, Type of car owned

Ratio Data

Temperature in Fahrenheit, Standardized exam score

Categories (no ordering or direction)

Ordered Categories (rankings, order, or scaling)

Differences between measurements but no true zero

Differences between measurements, true zero exists

EXAMPLES:

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.. Chap 1-12

Business Statistics Begin as Data!

store sales store sales store sales store sales store sales1 $4,610.19 11 $4,376.70 21 $5,466.46 31 $5,386.23 41 $4,247.052 $5,162.04 12 $4,980.50 22 $4,966.95 32 $4,898.44 42 $5,377.373 $5,090.04 13 $5,331.17 23 $4,984.81 33 $4,332.03 43 $5,167.414 $5,013.03 14 $4,406.93 24 $4,823.75 34 $4,774.19 44 $4,691.525 $4,981.06 15 $4,560.95 25 $5,538.26 35 $5,606.18 45 $5,280.086 $5,321.75 16 $5,304.02 26 $4,724.14 36 $4,484.85 46 $5,131.347 $4,913.79 17 $4,227.67 27 $4,736.50 37 $5,226.62 47 $5,379.698 $4,224.06 18 $5,213.50 28 $4,712.66 38 $5,107.49 48 $4,865.859 $5,109.23 19 $5,252.66 29 $5,695.59 39 $4,417.79 49 $3,980.63

10 $5,547.03 20 $5,553.03 30 $5,098.40 40 $5,692.39 50 $5,146.09

Sales for all 50 McSorley’s stores for December 31, 2005.

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.. Chap 1-13

Visualizing Data: the HistogramHistogram

0

2

4

6

8

10

12

14

Bin

Fre

qu

en

cy

Frequency

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.. Chap 1-14

Summarizing & Conveying Data

Minimum 3980.63

Maximum 5695.59

Range 1714.97Mean 4982.40Median 5051.54

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.. Chap 1-15

Inferring from a Sample

store sales store sales store sales store sales store sales1 $4,610.19 11 $4,376.70 21 $5,466.46 31 $5,386.23 41 $4,247.052 $5,162.04 12 $4,980.50 22 $4,966.95 32 $4,898.44 42 $5,377.373 $5,090.04 13 $5,331.17 23 $4,984.81 33 $4,332.03 43 $5,167.414 $5,013.03 14 $4,406.93 24 $4,823.75 34 $4,774.19 44 $4,691.525 $4,981.06 15 $4,560.95 25 $5,538.26 35 $5,606.18 45 $5,280.086 $5,321.75 16 $5,304.02 26 $4,724.14 36 $4,484.85 46 $5,131.347 $4,913.79 17 $4,227.67 27 $4,736.50 37 $5,226.62 47 $5,379.698 $4,224.06 18 $5,213.50 28 $4,712.66 38 $5,107.49 48 $4,865.859 $5,109.23 19 $5,252.66 29 $5,695.59 39 $4,417.79 49 $3,980.63

10 $5,547.03 20 $5,553.03 30 $5,098.40 40 $5,692.39 50 $5,146.09

59.280sdeviationstdsample46.5090xmeansample

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.. Chap 1-16

Sampling Distributions & Interval Estimates

x

If means of random samples of size 10 were compiled, they would have their own histogram.

This indicates a sampling distribution, and leads to an interval estimate for the population:

confidenceeifor

n

%95..,05.

]57.5352,83.4828[

87.26170.509010

51.42296.170.5090zx /2

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.. Chap 1-17

Inferring from Samples from Two Populations

29.5381xmeansample

store sales store sales store sales store sales store sales1 $5,848.23 11 $5,741.09 21 $4,344.04 31 $5,257.14 41 $5,787.472 $5,853.49 12 $5,057.03 22 $5,559.21 32 $6,416.79 42 $5,523.113 $4,851.46 13 $5,195.91 23 $5,161.21 33 $5,152.92 43 $4,908.604 $5,364.32 14 $4,191.21 24 $5,282.24 34 $5,630.53 44 $4,709.735 $5,268.38 15 $5,586.52 25 $5,430.77 35 $4,952.73 45 $5,908.286 $5,811.48 16 $5,635.64 26 $5,628.26 36 $4,486.57 46 $5,383.527 $5,322.21 17 $5,851.78 27 $4,561.28 37 $4,871.58 47 $5,647.858 $4,999.34 18 $5,120.53 28 $5,832.65 38 $5,440.68 48 $5,481.099 $5,625.81 19 $5,885.36 29 $4,261.30 39 $6,026.93 49 $5,360.95

10 $5,908.91 20 $4,990.95 30 $6,198.24 40 $5,140.08 50 $5,199.29

Sales for all 50 Wonder’s stores for December 31, 2005.

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.. Chap 1-18

Are you 95% sure that Wonder’s mean sales exceed McSorley’s?

Ho: M W; McSorley’s mean sales is no less than Wonder’s

Ha: M < W; McSorley’s mean sales is less than Wonder’s

867.4

5051.422

5051.422

0)29.538170.5090(

)()(

22

22

W

W

M

M

WMWM

nn

xxzstatistictest

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.. Chap 1-19

Are you 95% sure that Wonder’s mean sales exceed McSorley’s?

zz00

Area = .95Area = .95

z.05=-1.645

Do not reject Ho

Reject Ho

Compare test statistic z=-4.867 to critical value z.05=-1.645.

Conclusion: Reject Ho

z=-4.867