Final Exam Review Sheet - Final Exam Review | BIT 2405, Study notes of Introduction to Business Management

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BIT 2405 Quantitative Methods I

BIT 2405 Quantitative Methods I

Final Exam Preparation

Final Exam Preparation

Chapters 1 through 11.

Chapters 1 through 11.

Schedule This Week

December 8

th

.

Day Content Time/Location

Monday &

Tuesday

Review for Final

Regular class hours &

locations

Tuesday &

Wednesday

Help Sessions

Test 1, 2, & 3

Questions

TR 4:15 pm PAM 2030

F 10:10 am PAM 32

F 1:25 pm PAM 30

Thursday & Friday

NO CLASS:

Reading Day and

Exams Begin

Help Sessions:

Help Sessions:

Times & Places Posted

Times & Places Posted

on Blackboard in

on Blackboard in

Announcements

Announcements

Picture Day

Picture Day

Picture Day

Picture Day

Hawkes 10.xHawkes 10.x

Modules Due

Modules Due

Monday at 11:59pm

Monday at 11:59pm

Hawkes 10.x

Hawkes 10.x

Modules Due

Modules Due

Monday at 11:59pm

Monday at 11:59pm

DiscussionDiscussion

Board is

Board is

Open on BB

Open on BB

Discussion

Discussion

Board is

Board is

Open on BB

Open on BB

Schedule Next Week

December 15

th

.

Day Content Time/Location

Monday &

Tuesday

December 15 & 16

No Class

Other Exams

Wednesday:

December 17

FINAL EXAM

11:05 am – 1:05 pm

in

Hancock 100

Help Sessions:

Help Sessions:

Times & Places Posted

Times & Places Posted

on Blackboard in

on Blackboard in

Announcements

Announcements

Questions?

How the Online Quizzes & Homework

How the Online Quizzes & Homework

Grade Is Calculated.

Grade Is Calculated.

100

%

HomeworkPo ints%

10

i 1







i

GradeHW

3

%

QuizMean%

3

i 1







i

QuizGrade

Quiz & Homework Grade = QuizMean + HomeworkPoints

Quiz & Homework Grade = QuizMean + HomeworkPoints

Maximum Possible Grade Example:

Maximum Possible Grade Example:

00% on all three Quizzes & 100% on all 10 Optional Homework Se

00% on all three Quizzes & 100% on all 10 Optional Homework Se

10. 0 %

100

1 , 000

100

100

HomeworkPo ints%

10

i 1

  





i

100 %

3

300

3

100

QuizMean%

3

i 1

  





i

Quiz & Homework Grade = 100% + 10.0% = 110%

Quiz & Homework Grade = 100% + 10.0% = 110%

How the Hawkes Certification Grades Are

How the Hawkes Certification Grades Are

Calculated.

Calculated.

30 Hawkes Certifications Are Assigned

30 Hawkes Certifications Are Assigned

Points are assigned to each depending on when

Points are assigned to each depending on when

the certification was submitted

the certification was submitted

10 points for on-time

10 points for on-time

5 points for 1-day late

5 points for 1-day late

0 points for more than 1-day late or NOT

0 points for more than 1-day late or NOT

submitted

submitted

Lowest 3 scores are dropped

Lowest 3 scores are dropped

270

Points

HawkesGrad e%

27 Highest

i 1







i

Maximum Possible Grade Example:

Maximum Possible Grade Example:

10 Points on 27 Certifications = 270/270 = 100%

10 Points on 27 Certifications = 270/270 = 100%

Overall Course Grades

Overall Course Grades

If You Were Excused from One of the 3

If You Were Excused from One of the 3

Tests, Your Final Exam Counts 35%

Tests, Your Final Exam Counts 35%

of your Total Grade.

of your Total Grade.

Hawkes

Hawkes

Final Exam

Final Exam



Approximately 50 Multiple Choice Questions

Approximately 50 Multiple Choice Questions

95% Confidence Interval Estimate

95% Confidence Interval Estimate

45 ≤ #Questions ≤ 55

45 ≤ #Questions ≤ 55

• Covers Chapters 1 through 11.

Covers Chapters 1 through 11.

Approximately 15 questions each for the first

Approximately 15 questions each for the first

3 tests.

3 tests.

Approximately 10 questions on Chapter 10.

Approximately 10 questions on Chapter 10.

• Mostly “calculations” with looking up in Tables

Mostly “calculations” with looking up in Tables



2 Hours to Complete

2 Hours to Complete

Today Covers

Today Covers

WHAT

WHAT

Topics Are On The

Topics Are On The

Final Exam and

Final Exam and

NOT HOW

NOT HOW

to Answer

to Answer

Questions.

Questions.



To Understand HOW, Review

To Understand HOW, Review

• Optional Homework Problems: ~200 questions

Optional Homework Problems: ~200 questions

• Quizzes: ~75 questions

Quizzes: ~75 questions

•

Frequently Missed Questions (FMQs) from Tests

Frequently Missed Questions (FMQs) from Tests

1, 2 & 3 on Blackboard

1, 2 & 3 on Blackboard

• Lecture slides especially Test 1, 2 & 3 Prep PPTs

Lecture slides especially Test 1, 2 & 3 Prep PPTs

• Hawkes:

Hawkes: Do practice problems to remember

Do practice problems to remember

how to work problems for any of the topics.

how to work problems for any of the topics.

The VIDEO button during INSTRUCT is very

The VIDEO button during INSTRUCT is very

helpful on how to work problems.

helpful on how to work problems.

The online Quizzes & Optional Homework sets are

The online Quizzes & Optional Homework sets are

available through “My Grades” on Blackboard. Click

available through “My Grades” on Blackboard. Click

on your grade and you will be able to see your

on your grade and you will be able to see your

Today Covers

Today Covers

WHAT

WHAT

Topics Are On The

Topics Are On The

Final Exam and

Final Exam and

NOT HOW

NOT HOW

to Answer

to Answer

Questions.

Questions.



Figure out what you Don’t Know & Come to the Help

Figure out what you Don’t Know & Come to the Help

Sessions

Sessions

•

Review the questions you missed on Tests 1, 2, & 3

Review the questions you missed on Tests 1, 2, & 3

• Ask questions on how to work problems

Ask questions on how to work problems



I will post a PowerPoint video on Hypothesis Testing

I will post a PowerPoint video on Hypothesis Testing

this week.

this week.

•

I will email you when that’s posted.

I will email you when that’s posted.



I will revise the Final Exam Formula Sheet to add

I will revise the Final Exam Formula Sheet to add

some DESCRIPTIONS to help you identify formulas

some DESCRIPTIONS to help you identify formulas

• I will email you when that’s posted.

I will email you when that’s posted.

Test 1: Chapters 1 through 5

Test 1: Chapters 1 through 5

Chapter 1: Data and Statistics

Chapter 1: Data and Statistics



Know Population Parameters and Sample Statistics

Know Population Parameters and Sample Statistics

• e.g., σ compared to s

e.g., σ compared to s



Scales of Measure

Scales of Measure

• e.g., Interval vs Ratio: Categorical vs Quantitative

e.g., Interval vs Ratio: Categorical vs Quantitative

Chapter 2: Descriptive Statistics

Chapter 2: Descriptive Statistics



Summarize Categorical and Quantitative Data

Summarize Categorical and Quantitative Data

• Frequency Distribution

Frequency Distribution

• Relative Frequency & Percent Relative Frequency

Relative Frequency & Percent Relative Frequency

• Cumulative Relative Frequency & Cumulative

Cumulative Relative Frequency & Cumulative

Percent Relative Frequency

Percent Relative Frequency

Tables not

Tables not

Graphs

Graphs

Not On The Test

Not On The Test

Test 1: Chapters 1 through 5

Test 1: Chapters 1 through 5

Chapter 3: Numerical Measures

Chapter 3: Numerical Measures



Measures of Location

Measures of Location

• Calculate mean, mode, median, percentiles,

Calculate mean, mode, median, percentiles,

and quartiles

and quartiles



Measures of Variance

Measures of Variance

• Calculate range, interquartile range,

Calculate range, interquartile range,

variance, standard deviation, and coefficient

variance, standard deviation, and coefficient

of variation

of variation



Measures of Shape

Measures of Shape

• No z-scores, skewness, Chebychev’s,

No z-scores, skewness, Chebychev’s,

Emperical Rule nor Detecting Outliers

Emperical Rule nor Detecting Outliers

Not On The Test

Not On The Test

Test 1: Chapters 1 through 5

Test 1: Chapters 1 through 5

Chapter 4: Introduction to Probability

Chapter 4: Introduction to Probability



Understand experiment, sample space, sample

Understand experiment, sample space, sample

points, & events

points, & events

• Probability ranges from 0 to 1

Probability ranges from 0 to 1

• Percent Probability ranges from 0 to 100

Percent Probability ranges from 0 to 100



Counting rules for

Counting rules for

• Multistep

Multistep

• Combination

Combination

•

Permutation

Permutation



Assigning Probabilities

Assigning Probabilities

• Uniform

Uniform

• Relative Frequency

Relative Frequency

•

Subjective

Subjective

Not On The Test

Not On The Test

Test 1: Chapters 1 through 5

Test 1: Chapters 1 through 5

Chapter 4: Introduction to Probability

Chapter 4: Introduction to Probability



Events and their Probabilities

Events and their Probabilities

• Sum of the probabilities of the sample points

Sum of the probabilities of the sample points

in the event

in the event



Relationships of Events

Relationships of Events

• Compliment

Compliment

• Union & Intersection of 2 events

Union & Intersection of 2 events

Test 1: Chapters 1 through 5

Test 1: Chapters 1 through 5

Chapter 4: Introduction to Probability

Chapter 4: Introduction to Probability



Mutually Exclusive Events

Mutually Exclusive Events



Independent Events

Independent Events



Conditional Probability

Conditional Probability

If events

If events A

A and

and B

B are

are

mutually exclusive,

mutually exclusive,

P

P (

( A

A 

 B

B 

 = 0.

= 0.

If events

If events A

A and

and B

B are

are

mutually exclusive,

mutually exclusive,

P

P (

( A

A 

 B

B 

 = 0.

= 0.

IF

IF

P

P (

( A

A 

 B

B ) =

) = P

P (

( A

A )

) P

P (

( B

B )

)

Then A and B are INDEPENDENT

Then A and B are INDEPENDENT

IF

IF

P

P (

( A

A 

 B

B ) ≠

) ≠ P

P (

( A

A )

) P

P (

( B

B )

)

Then A and B are DEPENDENT

Then A and B are DEPENDENT

IF

IF

P

P (

( A

A 

 B

B ) =

) = P

P (

( A

A )

) P

P (

( B

B )

)

Then A and B are INDEPENDENT

Then A and B are INDEPENDENT

IF

IF

P

P (

( A

A 

 B

B ) ≠

) ≠ P

P (

( A

A )

) P

P (

( B

B )

)

Then A and B are DEPENDENT

Then A and B are DEPENDENT

( )

( | )

( )

P A B

P A B

P B





( )

( | )

( )

P A B

P A B

P B





P

P

(

(

A

A

|

|

B

B

) =

) =

P

P

(

(

A

A

)

)

P

P

(

(

A

A

|

|

B

B

) =

) =

P

P

(

(

A

A

)

)

P

P

(

(

B

B

|

|

A

A

) =

) =

P

P

(

(

B

B

)

)

P

P

(

(

B

B

|

|

A

A

) =

) =

P

P

(

(

B

B

)

)

Test 1: Chapters 1 through 5

Test 1: Chapters 1 through 5

Chapter 5: Discrete Probability Distributions

Chapter 5: Discrete Probability Distributions



Random Variable

Random Variable x

x



Discrete Probability Distribution Function

Discrete Probability Distribution Function



Expected Value

Expected Value



Variance

Variance

f

f (

(

x

x )

)

>

>

0

f 0

f (

(

x

x )

)

>

>

0

0





f

f (

(

x

x ) = 1

) = 1





f

f (

(

x

x ) = 1

) = 1

E

E

(

(

x

x ) =

) = 

=

= 

xf

xf (

(

x

x )

E )

E

(

(

x

x ) =

) = 

=

= 

xf

xf (

(

x

x )

)

f

f (

(

x

x ) = 1/

) = 1/

n

f n

f (

(

x

x ) = 1/

) = 1/

n

n

Discrete Uniform

Discrete Uniform

Distribution

Distribution

Var(

Var( x

x ) =

) =





22

=

=





(

(

x

x

-





)

)

22

f

f (

(

x

x )

Var( )

Var( x

x ) =

) =





22

=

=





(

(

x

x

-





)

)

22

f

f (

(

x

x )

)

Test 1: Chapters 1 through 5

Test 1: Chapters 1 through 5

Chapter 5: Discrete Probability Distributions

Chapter 5: Discrete Probability Distributions



Binomial Probability Distribution

Binomial Probability Distribution

•

Recognize Binomial Experiments

Recognize Binomial Experiments

• Denote

Denote x

x as the number of successes in the

as the number of successes in the n

n

trials

trials

Test 1: Chapters 1 through 5

Test 1: Chapters 1 through 5

Chapter 5: Discrete Probability Distributions

Chapter 5: Discrete Probability Distributions



Binomial Probability Distribution

Binomial Probability Distribution

• Binomial Probability Function

Binomial Probability Function

where:

where:

f

f (

(

x

x ) = the probability of

) = the probability of x

x successes in

successes in n

n trials

trials

n

n = the number of trials

= the number of trials

p

p = the probability of success on any one trial

= the probability of success on any one trial

with

with

x n x

p p

x

n

f X x





















(  )  ( 1 )

!  !

!

x n x

n

x

n





















Don’t confuse n and p

Don’t confuse n and p

with sample size

with sample size

and proportion.

and proportion.

Test 1: Chapters 1 through 5

Test 1: Chapters 1 through 5

Chapter 5: Discrete Probability Distributions

Chapter 5: Discrete Probability Distributions



Binomial Probability Distribution

Binomial Probability Distribution

• Expected Value

Expected Value

• Variance

Variance

• Standard Deviation

Standard Deviation

E

E

(

(

x

x ) =

) =





=

=

np

np





2

2

=

=

np

np (

(





p

p )

)

  np ( 1  p )

Test 2: Chapters 6 through 8

Test 2: Chapters 6 through 8

Chapter 6.2: Normal Probability Distribution

Chapter 6.2: Normal Probability Distribution



Understand Characteristics

Understand Characteristics



Mean, Mode, Median

Mean, Mode, Median

Test 2: Chapters 6 through 8

Test 2: Chapters 6 through 8

Chapter 6.2: Normal Probability Distribution

Chapter 6.2: Normal Probability Distribution



Understand characteristics, for example

Understand characteristics, for example

• Symmetrical

Symmetrical

• Defined by 2 parameters, Mean and

Defined by 2 parameters, Mean and

Standard Deviation

Standard Deviation



Convert X values to Standard Normal

Convert X values to Standard Normal

Distribution

Distribution

• Calculate and look up probabilities

Calculate and look up probabilities



 



X

z

Test 2: Chapters 6 through 8

Test 2: Chapters 6 through 8

Chapter 7: Sampling and Sampling Distributions

Chapter 7: Sampling and Sampling Distributions



Point Estimation

Point Estimation



Sampling Distributions of sample mean and

Sampling Distributions of sample mean and

sample proportion.

sample proportion.

• If , use otherwise

If , use otherwise



















n

N

N n

x























n

N

N n

x





n

x



 

n

x



 0. 05  

N

n

x

x

x

z



 



Test 2: Chapters 6 through 8

Test 2: Chapters 6 through 8

Chapter 8: Interval Estimation

Chapter 8: Interval Estimation



Population Mean

Population Mean σ

σ known

known



Population Mean

Population Mean σ

σ unknown

unknown



Determining the Sample Size to achieve a specific

Determining the Sample Size to achieve a specific

Margin of Error

Margin of Error



Population Proportion

Population Proportion

• p* is the planning number

p* is the planning number

• Use 0.5 if no better estimate is available

Use 0.5 if no better estimate is available

Point Estimate +/

Point Estimate +/ 



Margin of Error

Margin of Error

If the calculated value of n is not a

If the calculated value of n is not a

whole number, ROUND UP!

whole number, ROUND UP!

2 * *

/ 2

2

( z ) p (1 p )

n

E







2 * *

/ 2

2

( z ) p (1 p )

n

E







Test 3: Chapters 9 & 11.1

Test 3: Chapters 9 & 11.1

Chapter 9: Hypothesis Testing

Chapter 9: Hypothesis Testing



Population Mean:

Population Mean: σ

σ known

known



Population Mean:

Population Mean: σ

σ unknown

unknown



Population Proportion

Population Proportion

Chapter 11.1 Population Variance

Chapter 11.1 Population Variance



Population Variance and Standard Deviation

Population Variance and Standard Deviation

• Interval Estimate

Interval Estimate

• Hypothesis Testing

Hypothesis Testing

Interval Estimation:

Interval Estimation:

( ) ( )

/ ( / )

n  s n s

 





2

2

2

2

2

1 2

2







 

( ) ( )

/ ( / )

n  s n s

 





2

2

2

2

2

1 2

2







 

2 2

2 2

/ 2 (1 / 2)

( n 1) s ( n 1) s

 



 



 

 

2 2

2 2

/ 2 (1 / 2)

( n 1) s ( n 1) s

 



 



 

 













2

2

Only

Only σ

σ

22

&

& σ

σ

1. Determine whether it’s variance or standard

Determine whether it’s variance or standard

deviation

deviation

Calculate

Calculate α

α /2 and the Degrees of Freedom (d.f.)

/2 and the Degrees of Freedom (d.f.)

(n-1)

(n-1)

3. Look up the two

Look up the two X

X

2

2

values and

values and

Crunch the numbers.

Crunch the numbers.