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20+FinalExamPrep - BIT 2405 Quantitative Methods I BIT 2405...

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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 2-4pm 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(A|B) = P(A) Not OnB|A) = 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 σ-known σ-unknown z = x−µ obs σ / n 0 Z-Tables σ Z-Tables t = x −µ obs s / n ˆ p − p0 = σ pobs 0 T-Tables z obs σp obs = p 0 (1 − p 0 ) n 2 X2-Tables ( 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 σ-known Z-Tables σ-unknown T-Tables Z-Tables σ 2 X2-Tables Keep Track of What You’re Looking Up. p μ σ-known Z-Tables • Symmetrical Symmetrical • Centered on 0 Centered • Lower Tail Given L ower σ-unknown Z-Tables σ 2 Keep Track of What You’re Looking Up. p μ σ-known • • • • • σ-unknown Symmetrical Symmetrical Centered on 0 Centered Upper Tail Given Upper Degrees of Freedom Degrees Columns are Areas Columns T-Tables σ 2 Keep Track of What You’re Looking Up. p μ σ-known σ-unknown • 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 X2-Tables 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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