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My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z PowerPoint Presentation

My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z

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Set your clicker to channel 03

My last name starts with a

letter somewhere between

A. A – D

B. E – L

C. M – R

D. S – Z

MGMT 276: Statistical Inference in Management

Welcome

http://www.thedailyshow.com/video/index.jhtml?videoId=188474&title=an-arab-family-man

Chapters 5 - 9 in Lind book

& Chapters 10, 11, 12 & 14 in Plous book:

Lind

Chapter 5: Survey of Probability Concepts

Chapter 6: Discrete Probability Distributions

Chapter 7: Continuous Probability Distributions

Chapter 8: Sampling Methods and CLT

Chapter 9: Estimation and Confidence Interval

Plous

Chapter 10: The Representativeness Heuristic

Chapter 11: The Availability Heuristic

Chapter 12: Probability and Risk

Chapter 14: The Perception of Randomness

We’ll be jumping around some…we will start with chapter 7

Homework due next class - (Due September 29th)

Complete probability worksheet available on class website

Please double check – All cell phones other electronic devices are turned off and stowed away

study guide

By the end of lecture today9/27/11Measures of variability

Standard deviation and Variance

Estimating standard deviation

Exploring relationship between mean and variability

Law of Large NumbersEmpirical, classical and subjective approaches

Probability of an event

Complement of an event; Union of two events

Intersection of two events; Mutually exclusive events

Collectively exhaustive events

Conditional probability

Central Limit Theorem

Go to

table

33-30

z = 1.5

z =

.4332

2

.9332

.4332

.5000

24

36

32

28

34

26

30

77th percentile

Go to

table

nearest z = .74

.2700

x = mean + z σ = 30 + (.74)(2) = 31.48

.7700

.27

.5000

24

36

?

28

34

26

30

31.48

13th percentile

Go to

table

nearest z = 1.13

.3700

x = mean + z σ = 30 + (-1.13)(2) = 27.74

.37

.50

.13

?

24

36

32

27.74

34

26

30

Please use the following distribution with a mean of 200

and a standard deviation of 40.

Find the area under the curve between scores of 200 and 230.

Start by filling in the desired information on curve 20 (to the right)(Note this one will require you to calculate a z-score for a raw score of 230 and use the z-table)

Go to

table

230-200

z = .75

z =

.2734

40

.2734

80

320

240

160

280

120

200

Normal Distribution has a mean of 50 and standard deviation of 4.

Determine value below which 95% of observations will occur.Note: sounds like a percentile rank problem

1.64

okay too

Go to

table

.4500

nearest z = 1.65

x = mean + z σ = 50 + (1.65)(4) = 56.60

.9500

.4500

.5000

38

62

54

46

58

?

42

50

56.60

Normal Distribution has a mean of $2,100 and of 4.s.d. of $250.

What is the operating cost for the lowest 3% of airplanes.Note: sounds like a percentile rank problem = find score for 3rd percentile

Go to

table

.4700

nearest z = - 1.88

x = mean + z σ = 2100 + (-1.88)(250) = 1,630

.0300

.4700

?

2100

1,630

Normal Distribution has a mean of 195 and standard deviation of 8.5.

Determine value for top 1% of hours listened.

Go to

table

.4900

nearest z = 2.33

x = mean + z σ = 195 + (2.33)(8.5) = 214.805

.4900

.0100

.5000

195

?

214.8

Try this one: of 8.5.

Please find the (2) raw scores that border exactly the middle 95% of the curve

Mean of 30 and standard deviation of 2

Go to

table

.4750

nearest z = 1.96

mean + z σ = 30 + (1.96)(2) = 33.92

Go to

table

.4750

nearest z = -1.96

mean + z σ = 30 + (-1.96)(2) = 26.08

.9500

.475

.475

26.08

33.92

?

?

24

32

36

28

30

Variability and means of 8.5.

Remember, there is an implied axis measuring frequency

f

38 40 44 48 52 56 58

f

40 44 48 52 56

. of 8.5.

Writing AssignmentComparing distributions (mean and variability)- Think of examples for these three situations
- same mean but different variability
- same variability but different means
- same mean and same variability (different groups)
- estimate standard deviation
- calculate variance
- for each curve find the raw score for the z’s given

What is probability of 8.5.

1. Empirical probability: relative frequency approach

Number of observed outcomes

Number of observations

Probability of getting into an educational program

Number of people they let in

400

66% chance of getting admitted

Number of applicants

600

Probability of getting a rotten apple

5% chance of

getting a rotten

apple

Number of rotten apples

5

Number of apples

100

What is probability of 8.5.

1. Empirical probability: relative frequency approach

Number of observed outcomes

Number of observations

Probability of hitting the corvette

Number of carts that hit corvette

Number of carts rolled

182

= .91

200

91% chance of hitting a corvette

2. Classic probability: a priori probabilities based on logic

rather than on data or experience. We assume we know

the entire sample space as a collection of equally likely

outcomes (deductive rather than inductive).

Number of outcomes of specific event

Number of all possible events

In throwing a die what is the probability of getting a “2”

Number of sides with a 2

1

16% chance of getting a two

=

Number of sides

6

In tossing a coin what is probability of getting a tail

1

Number of sides with a 1

50% chance

of getting a tail

=

2

Number of sides

3. Subjective probability: based on someone’s personal logic

judgment (often an expert), and often used when empirical

and classic approaches are not available.

There is a 5% chance that Verizon will

merge with Sprint

Bob says he is 90% sure he could swim across the river

If logicP(A) = 0, then the event cannot occur.

If P(A) = 1, then the event is certain to occur.

The probability of an event is the relative likelihood that the event will occur.

The probability of event A [denoted P(A)], must lie

within the interval from 0 to 1:

0 <P(A) < 1

Probability logic

The probabilities of all simple events must sum to 1

P(S) = P(E1) + P(E2) + … + P(En) = 1

For example, if the following number of purchases were made by

What is the complement of the probability of an event logic

- The probability of event A = P(A).
- The probability of the complement of the event A’ = P(A’)
- A’ is called “A prime”

- Complement of A just means probability of “not A”
- P(A) + P(A’) = 100%
- P(A) = 100% - P(A’)
- P(A’) = 100% - P(A)

Probability of

getting a rotten apple

5% chance of “rotten apple”

95% chance of “not rotten apple”

100% chance of rotten or not

Probability of getting

into an educational program

66% chance of “admitted”

34% chance of “not admitted”

100% chance of admitted or not

Two mutually exclusive characteristics: if the occurrence of any one of them automatically implies the non-occurrence of the remaining characteristic

Two events are mutually exclusive if they cannot occur at the same time (i.e. they have no outcomes in common).

Two propositions that logically cannot both be true.

NoWarranty

Warranty

For example, a car repair is either covered by the warranty (A) or not (B).

http://www.thedailyshow.com/video/index.jhtml?videoId=188474&title=an-arab-family-man

Collectively Exhaustive Events occurrence of any one of them automatically implies the non-occurrence of the remaining characteristic

Events are collectively exhaustive if their union isthe entire sample space S.

Two mutually exclusive, collectively exhaustive events are dichotomous (or binary) events.

For example, a car repair is either covered by the warranty (A) or not (B).

NoWarranty

Warranty

No occurrence of any one of them automatically implies the non-occurrence of the remaining characteristicWarranty

Satirical take on being “mutually exclusive”

Warranty

Recently a public figure in the heat of the moment inadvertently made a statement that reflected extreme stereotyping that many would find highly offensive. It is within this context that comical satirists have used the concept of being “mutually exclusive” to have fun with the statement.

Decent ,

family man

Arab

Transcript:

Speaker 1:

“He’s an Arab”

Speaker 2:

“No ma’am, no ma’am.

He’s a decent, family

man, citizen…”

http://www.thedailyshow.com/video/index.jhtml?videoId=188474&title=an-arab-family-man

Thank you! occurrence of any one of them automatically implies the non-occurrence of the remaining characteristic

See you next time!!

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