Unformatted text preview: BIT 2405 Quantitative Methods I
BIT 2405 Quantitative Methods I
Final Exam Preparation
Chapters 1 through 11.1 This Week.
This Week.
Lectures Hawkes Today FINAL EXAM
FINAL
REVIEW
REVIEW COURSE &
COURSE
INSTRUCTOR
EVALUATIONS
EVALUATIONS
@ End of Class Optional HW10 is posted on Scholar along with some
Optional
help on #9 posted in the Discussion Board on
Blackboard.
Blackboard. Next Week and Beyond.
Next Week and Beyond. HELP SESSION on
HELP
Tuesday, December
8th.
EARLY FINAL EXAM
24pm TORG2150
Email me by Tuesday
Email
12/8 @ 9am if you want
to take your final Early
to Lectures The LAST HLS
Certifications! Hawkes Optional HW10 Due
Optional
@ 9am on
Wednesday,
December 16th.
December FINAL EXAM Wednesday, December
FINAL
16th
16
11:05am 1:05pm TORG 2150
11:05am Questions?
Questions? Final Exam
Final Exam
s At least 50 Multiple Choice Questions 100% Confidence Interval Estimate 50 ≤ #Questions ≤ 55 • Covers Chapters 1 through 11.1
• Approximately 15 questions each for the material on the first 3 tests.
• Approximately 7 questions on Chapter 10. •
s Mostly “calculations” with looking up in Tables 2 Hours to Complete Today Covers WHAT Topics Are On The Final Today Covers Exam and NOT HOW to Answer Questions. s To Understand HOW, Review
• Optional Homework Problems: ~200 questions
• Quizzes: ~75 questions
• Your Test Feedback in Post’Em & FMQs from Tests 1, 2 & 3 on Scholar
• Lecture slides especially Test 1, 2 & 3 Prep PPTs
• Hawkes: Practice problems for topics. Set up a practice test (Instructions in Resources>Hawkes Help on Scholar.
• Text: SelfTest Problems in the Chapters. NOTE: We calculate two population problems differently than the Text. Y our online Quizzes & Optional Homework sets are available
Your
through “ Tests & Quizzes” on Scholar.
through Today Covers WHAT Topics Are On The Final Today Covers Exam and NOT HOW to Answer Questions. s Figure out what you Don’t Know & Come to the Help Sessions on Tuesday
• Review the questions you missed on Tests 1, 2, & 3
• Ask questions on how to work problems s I’ll monitor the Discussion Board on Blackboard until about 10pm on Tuesday Night before the Final on Wednesday. Test 1: Chapters 1 through 5
Test 1: Chapters 1 through 5 s s Chapter 1: Data and Statistics
Know Population Parameters and Sample Statistics
• e.g., σ compared to s
Not On The Test
Scales of Measure
• e.g., Interval vs Ratio: Categorical vs Quantitative Tables not
Tables
Graphs
Graphs
s Chapter 2: Descriptive Statistics
Summarize Categorical and Quantitative Data
• Frequency Distribution • Relative Frequency & Percent Relative Frequency
• Cumulative Relative Frequency & Cumulative Percent Relative Frequency Test 1: Chapters 1 through 5
Test 1: Chapters 1 through 5 s s s Chapter 3: Numerical Measures
Measures of Location
• Calculate mean, mode, median, percentiles, and quartiles
Measures of Variance
• Calculate range, interquartile range, variance, standard deviation, and coefficient of variation
Measures of Shape
• No zscores, skewness, Chebychev’s, Emperical Rule nor Detecting Outliers Not On The Test Test 1: Chapters 1 through 5
Test 1: Chapters 1 through 5
s s s Chapter 4: Introduction to Probability
Understand experiment, sample space, sample points, & events
• Probability ranges from 0 to 1
• Percent Probability ranges from 0 to 100
Counting rules for • Multistep
• Combination
• Permutation
Assigning Probabilities
• Uniform
• Relative Frequency
Not On The Test
• Subjective Test 1: Chapters 1 through 5
Test 1: Chapters 1 through 5
s s Continuing with Chapter 4: Introduction to Probability
Events and their Probabilities
• Sum of the probabilities of the sample points in the event
Relationships of Events
• Compliment
• Union & Intersection of 2 events Not On The Test Test 1: Chapters 1 through 5
Test 1: Chapters 1 through 5
s s Continuing with Chapter 4: Introduction to Probability
Mutually Exclusive Events If events A and B are mutually exclusive, P(A ∩ B) = 0. Independent Events
IF P(A ∩ B) = P(A)P(B)
Then A and B are INDEPENDENT
IF P(A ∩ B) ≠ P(A)P(B)
Then A and B are DEPENDENT s Conditional Probability P(AB) = P(A) Not OnBA) = P(B)
P( The Test P( A ∩ B)
P( A  B) =
P( B) Test 1: Chapters 1 through 5
Test 1: Chapters 1 through 5 s
s Chapter 5: Discrete Probability Distributions
Random Variable x
Discrete Probability Distribution Function
f(x) > 0 s Σ f(x) = 1 Expected Value
E(x) = µ = Σ xf(x) s Variance
Var(x) = σ 2 = Σ (x µ )2f(x) Discrete Uniform Distribution f(x) = 1/n Test 1: Chapters 1 through 5
Test 1: Chapters 1 through 5 s Chapter 5: Discrete Probability Distributions
Binomial Probability Distribution
• Recognize Binomial Experiments • Denote x as the number of successes in the n trials Test 1: Chapters 1 through 5
Test 1: Chapters 1 through 5 s Chapter 5: Discrete Probability Distributions
Binomial Probability Distribution
• Binomial Probability Function n xi
f ( x i ) = p (1 − p )( n − x i )
x i where: f(x) = the probability of x successes in n trials n = the number of trials p = the probability of success on any one trial n
n!
with = x i x i !(n − x i )! Test 1: Chapters 1 through 5
Test 1: Chapters 1 through 5 s Chapter 5: Discrete Probability Distributions
Binomial Probability Distribution
• Expected Value
E(x) = µ = np • Variance σ 2 = np(1 − p) • Standard Deviation σ = np(1 − p ) Test 2: Chapters 6 through 8
Test 2: Chapters 6 through 8
s Chapter 6.2: Normal Probability Distribution
Understand Characteristics
s Mean, Mode, Median Test 2: Chapters 6 through 8
Test 2: Chapters 6 through 8
s s Chapter 6.2: Normal Probability Distribution
Understand characteristics, for example
• Symmetrical
• Defined by 2 parameters, Mean and Standard Deviation
Convert x values to Standard Normal Distribution
• Calculate and look up probabilities x −µ
z=
σ Test 2: Chapters 6 through 8
Test 2: Chapters 6 through 8
Chapter 7: Sampling and Sampling Distributions
s Point Estimation s Sampling Distributions of sample mean and sample proportion. • σ
σx =
If n/N ≤ 0.05 , use otherwise
n x−µ
zx =
σx N − n σ σx = N −1 n Test 2: Chapters 6 through 8
Test 2: Chapters 6 through 8
Chapter 8: Interval Estimation
Point Estimate +/− Margin of Error
s
s
s Population Mean σ known
Population Mean σ unknown
Determining the Sample Size to achieve a specific Margin of Error
I f the calculated value of n is not a whole
If
number,
number, s Population Proportion
• p* is the planning number • ROUND UP! ( zα / 2 )2 p* (1 − p* )
n=
E2 Use 0.5 if no better estimate is available Test 3: Chapters 9 & 11.1
Test 3: Chapters 9 & 11.1 s
s
s s Chapter 9: Hypothesis Testing
Population Mean: σ known
Population Mean: σ unknown
Population Proportion
Chapter 11.1 Population Variance
Population Variance and Standard Deviation
• Interval Estimate
• Hypothesis Testing Interval Estimation: σ and σ2
Interval Estimation: σ 2 ( n − 1) s2
( n − 1) s2
≤ σ2 ≤ 2
2
χ α /2
χ (1− α / 2) 1.
2.
3.
4. σ (n − 1) s 2
(n − 1) s 2
≤σ ≤
2
2
χα /2
χ (1−α / 2) Determine whether it’s variance or standard deviation
Calculate α/2 and the Degrees of Freedom (df) (n1)
Look up the two X2 values and Crunch the numbers. Hypothesis Testing
1. Three Basic Forms of the Null Hypothesis
whether it’ s μ, p, or σ.
p, Determine the basic test required & SKETCH IT! H 0 : µ ≥ µ0 H 0 : µ ≤ µ0 H 0 : µ = µ0 Onetailed
(lowertail) Onetailed
(uppertail) Twotailed α α α/2 α/2 Keep Track of What Population Parameter You Are Working With. p μ
σknown σunknown z = x−µ
obs σ / n
0 ZTables σ ZTables t
= x −µ
obs s / n ˆ
p − p0
=
σ pobs 0 TTables z obs
σp obs = p 0 (1 − p 0 )
n 2 X2Tables ( n − 1) s 2
χ2 =
σ2
0
obs Keep Track of What Test Is Needed.
1. Determine the basic test required & SKETCH IT! H 0 : µ ≥ µ0 H 0 : µ ≤ µ0 H 0 : µ = µ0 Onetailed
Onetailed
(lowertail) Onetailed
(uppertail) Twotailed α α α/2 α/2 Keep Track of What You’re Looking Up. p μ
σknown
ZTables σunknown
TTables ZTables σ 2 X2Tables Keep Track of What You’re Looking Up. p μ
σknown
ZTables
• Symmetrical
Symmetrical
• Centered on 0
Centered
• Lower Tail Given
L ower σunknown ZTables σ 2 Keep Track of What You’re Looking Up. p μ
σknown •
•
•
•
• σunknown Symmetrical
Symmetrical
Centered on 0
Centered
Upper Tail Given
Upper
Degrees of Freedom
Degrees
Columns are Areas
Columns TTables σ 2 Keep Track of What You’re Looking Up. p μ
σknown σunknown • NOT Symmetrical
NOT
• NOT Centered on 0
NOT
•All Positive Values
• Upper Tail Given
Upper
• Degrees of Freedom
Degrees
• Columns are Areas
Columns σ 2 X2Tables New Material: Chapter 10
New Material: Chapter 10 Chapter 10:
Chapter 10: Statistical Inference About Means and Proportions With Two Populations 10.1 Inferences About the Difference Between Two Population Means: σ 1 and σ 2 Known 10.2 Inferences About the Difference Between Two Population Means: σ 1 and σ 2 Unknown
10.3 Inferences About the Difference Between Two Population Means: Matched Samples Life Is Like Guitar Hero
Life Is Like Guitar Hero THANK YOU for this Semester!
THANK YOU for this Semester!
Have a GREAT Holiday and
Please YELL TO ME next Spring! Questions?
Questions?
Course Evaluations Next… Instructor Evaluations
Instructor Evaluations
s Do NOT PUT YOUR NAME or SID on the evaluation form. They are anonymous. s Put “R. Martin Jones” in the name box... name of Instructor. s Evaluations need to be grouped by CRN when you turn them in. I’ve got sheets with the DAY/TIME and CRN on them for you to stack your evaluation with the CRN you are officially in. s Instructor Evaluations
Instructor Evaluations
s I need a volunteer (or two) to • hand out the evaluations,
• collect the completed evaluations, and
• turn them into the BIT Department, 1007 Pamplin s Give me just a minute to shut down the overhead and leave. s THANK YOU for taking the time to do this! ...
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This note was uploaded on 08/30/2011 for the course ART 3514 taught by Professor Dhbannan during the Summer '03 term at Virginia Tech.
 Summer '03
 DHBannan

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