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### Homework1key

Course: STAT 311, Spring 2012
School: Purdue University -...
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Word Count: 931

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1 Homework (14 pts + 1 bonus) due Jan 21 (1 pt. bonus) Q0. Why were the earrings that I wore to class today relevant to today's lecture The earrings that I wore are dice (clear 6 sided dice to be specific). (3 pts.) 1.4. The following table provides a frequency distribution (in thousands) for the number of rooms in U.S. housing units. Rooms No. Units 1 471 2 1,470 3 11,715 4 23,468 5 24,476 6 21,327 7 13,782 8+...

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1 Homework (14 pts + 1 bonus) due Jan 21 (1 pt. bonus) Q0. Why were the earrings that I wore to class today relevant to today's lecture The earrings that I wore are dice (clear 6 sided dice to be specific). (3 pts.) 1.4. The following table provides a frequency distribution (in thousands) for the number of rooms in U.S. housing units. Rooms No. Units 1 471 2 1,470 3 11,715 4 23,468 5 24,476 6 21,327 7 13,782 8+ 15,647 If a U.S. housing unit is selected at random, find the probability that it has Total number of units, Total = 471 + 1,470 + 11,715 + 23,468 + 24,476 + 21,327 + 13,782 + 15,647 = 112,356 a) four rooms. No of units with 4 rooms 23,468 = =0.209 total 112,356 b) more than four rooms. No of units with 5 rooms and 6 rooms and 7 rooms and 8 or more rooms total 24,476 + 21,327 + 13,782 + 15,647 75,232 = = =0.670 112,356 112,356 c) one or two rooms No of units with 1 room or 2 rooms 471 + 1,470 1,941 = = = 0.017 total 112,356 112,356 d) fewer than one room. Since all housing units have at least one room, this is the empty set, \ e) one or more rooms. Since all of the units have one or more rooms, this is the whole sample space or 1. f) Identify the population under consideration. The population is the housing units in the U.S. 1 (1.5 pt.) 1.10. Use the frequentist interpretation of probability to interpret each statement. a) The probability is 0.314 that the gestation period of a woman will exceed 9 months. Looking at a large number of pregnant women, 314 out of 1000 women will have gestation periods of longer than 9 months. b) The probability is 2/3 that the favorite in a horse race finishes in the money (first, second, or third place). Looking at a large number of horse races, 66 out of 100 favorites will be end up in first, second or third place. c) The probability is 0.40 that a traffic fatality involves an intoxicated or alcohol-impaired driver or nonoccupant. Looking at a large number of traffic accidents that involve fatalities, 40 out of 100 will involve an alcohol impaired driver or an alcohol impaired nonoccupant. (2 pts.) 1.18. Let U = R and, for each n N, define An = [0,1/n]. a) Determine 4 A n-1 n 4 A n-1 n 4 A n-1 n and 4 A . n-1 n = [0, 1/1] [0,1/2] [0,1/3] [0,1/4] = [0,1/4] = [0, 1/1] U [0,1/2] U [0,1/3] U [0,1/4] = [0,1] A n-1 n b) Determine A n-1 n and A . n-1 n = [0, 1/1] [0,1/2] [0,1/3] [0,1/4] .... The left side is bounded at 0. The right side gets smaller and smaller but never quite reaches 0. Therefore the answer is {0} (no interval) 4 A = [0, 1/1] U [0,1/2] U [0,1/3] U [0,1/4] U ... n-1 n The left sides is bounded at 0, The right side will be the largest interval which is bounded at 1. Therefore, the answer is [0,1]. 2 (2 pt.) 1.27(a only). Refer to the distributive as laws, given in Proposition 1.2 on page 12. a) Verify parts (a) and (b) by using Venn diagrams. Proposition 1.2. Distributive Laws Let A, B, and C be subsets of U, Then a) A (B U C) = (A B) U (A C) A B A B BUC C A (B UC) C A B A B A B AB C C AC (A B) U (A C) C b) A U (B C) = (A U B) (A U C) A B A B BC C C A U (B C) A B A B A B AUB C C AUC (A U B) (A U C) C 3 (0.5 pt.) 1.15. Draw a Venn diagram showing three subsets, A, B, and C, such that no two are disjoint but that A B C = \. There are many ways that this can be drawn, one way is: A B C (3 pt.) 2.4 (6-sided die). Suppose that one die is rolled and that you observe the number of dots facing up. a) Obtain a sample space for this random experiment whose elements are integers. The sample space includes all of the possible outcomes or = {1, 2, 3, 4, 5, 6} b) Determine as a subset of the sample space each of the events A = die comes up even, B = die comes up at least 4, C = die comes up at most 2, and D = die comes up 3. A = {2, 4, 6} B = {4, 5, 6} C = {1, 2} D = {3} c) Determine as a subset of the sample space and describe in words each of the events Ac, A B, and B U C. Ac = {1, 3, 5} which is everything but A OR die comes up odd A B = {4, 6} which is everything that is in A and B OR the die is even and at least 4. B U C = {1, 2, 4, 5, 6} which is the die is NOT 3. f) Describe in words each of the events: {5}, {1, 3, 5}, and {1, 2, 3, 4}. {5}: The event that the die comes up 5. {1, 3, 5}: The event that the die comes up odd. {1, 2, 3, 4}: The event that the die comes up at most 4. (2 pts.) 2.10. This exercise considers two random experiments involving the repeated tossing of a coin. Note: You may assume that eventually a head will be tossed. a) If the coin is tossed until the first time a head appears, find the sample space. = {H, TH, TTH, TTTH, ...} This is the sample space where all the tosses are T except for the last one. b) If the coin is tossed until the second time a head appears, find the sample space. = {HH, THH, HTH, TTHH, THTH, HTTH, ...} This is the sample space where the last toss is a H, and there is only one H in the beginning tosses. 4 c) For the experiment in part (a), express the event that the coin is tossed exactly six times in the form {....}, where in place of "...." you list all of the outcomes in that event. E = {TTTTTH} Since the sample space is all tails except for the last toss, this event occurs if you toss 5 tails and then a H. d) Repeat part (c) for the experiment described in part (b). E = {TTTTHH, TTTHTH, TTHTTH, THTTTH, HTTTTH} In this sample space, the last toss is H and there is one other H tossed. Therefore, the first 5 tosses consist of 4 T and 1 H. 5
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Purdue University - Main Campus - STAT - 311
Homework 2 (13 points) due Jan 27(1.3 pts.) 2.4 (6-sided die)de. Suppose that one die is rolled and that you observe the number of dots facing up. From the last problem set: The sample space includes all of the possible outcomes or = cfw_1, 2, 3, 4, 5, 6
Purdue University - Main Campus - STAT - 311
Homework 3 (15 points) due Feb. 3.(1 pt.) 2.42. A commuter train arrives punctually at a station every half hour. Each morning, a commuter named John leaves his house and casually strolls to the strain station. Find the probability that John waits for th
Purdue University - Main Campus - STAT - 311
Homework 4 (11.5 points) due Feb. 10(1 pt.) 3.34ab A club has 14 members. a) How many ways can a governing committee of size 3 be chosen? This is without replacement because once a person is on the committee; he can't be on it again. This is unordered be
Purdue University - Main Campus - STAT - 311
Homework 5 (12 points) due Feb. 17(1.2 pt.) 4.4abc. The following table provides a frequency distribution, with frequencies in thousands, for the number of rooms in U.S. housing units. (Note: this is the same table as was used in problem 1.4.) Rooms No.
Purdue University - Main Campus - STAT - 311
SET DEFINITIONS1. 5. 9. 13. Item set 2. 6. Definition collection of objects 3. 7. Designation cfw_1,3, 5,7 4. 8. example my deck of cards is a set of cardsEmpty set 0. 1 Subset 14.16.Equal sets7. 120.Proper subset 21.a set has nothing in it 11. A i
Purdue University - Main Campus - STAT - 501
Stat 501Experimental Statistics IHandoutsPrint off the following:Syllabus ScheduleAs we go along:Posted lectures Homeworks Other handouts and review topicsAbout SAS Read the Introduction to SAS handout if desired.intro.sas is the file with the c
Purdue University - Main Campus - STAT - 501
Section 1.2Describing Distributions with NumbersQuantitative DataMeasuring CenterMean MedianMeasuring SpreadQuartiles Five Number Summary Standard deviationBoxplotsMeasures of CenterThe meanThe arithmetic mean of a data set (average value) Denot
Purdue University - Main Campus - STAT - 501
Section 1.3The Normal DistributionsTopicsDensity curves Normal distributions The 68-95-99.7 rule The standard normal distribution Normal distribution calculations Standardizing observations Normal quantile plotsDensity curvesDensity curveImagine a s
Purdue University - Main Campus - STAT - 501
Sections 2.1-2.2Looking at Data-RelationshipsData with two or more variables:Response vs Explanatory variables Scatterplots Correlation Regression lineAssociation between a pair of variablesAssociation: Some values of one variable tend to occur more
Purdue University - Main Campus - STAT - 501
Chapter 2 highlightsAssociation and CausationAssociation between a pair of variablesAssociation: Some values of one variable tend to occur more often with certain values of the other variable Both variables measured on same set of individuals Examples:
Purdue University - Main Campus - STAT - 501
Section 5.2Sampling Distribution for Counts and ProportionsPreviewPopulation distribution vs. sampling distribution Binomial distributions for sample counts Finding binomial probabilities: tables Binomial mean and standard variation Sample proportions
Purdue University - Main Campus - STAT - 501
Introduction to Inference Section 6.1Estimating with ConfidenceIntroductionDistinguish chance variations from permanent features of a phenomenon:Give SAT test to a SRS of 500 California seniors samplemean = 461 What does it say about the mean SAT sc
Purdue University - Main Campus - STAT - 501
Section 7.1Inference for the mean of a populationChange: Population standard deviation () is now unknown The t distribution One-sample t confidence interval One-sample t test Matched pairs t procedures Robustness of t proceduresThe t distribution:The
Purdue University - Main Campus - STAT - 501
Section 8.1Inference for a Single ProportionRecall: Population ProportionLet p be the proportion of &quot;successes&quot; in a population. A random sample of size n is selected, and X is the count of successes in the sample. Suppose n is small relative to the po
Purdue University - Main Campus - STAT - 501
Chapter 9Two categorical variables. Data Analysis and Inference for Two-Way TablesTopicsImportant change: We switch from quantitative variables to categorical variables describing relations in two-way tables marginal distributions conditional distribut
Purdue University - Main Campus - STAT - 501
Section 10.1Simple Linear RegressionA continuation of Chapter 2Statistical model for linear regression Data for simple linear regression Estimation of the parameters Confidence intervals and significance tests Confidence intervals for mean response vs.
Purdue University - Main Campus - STAT - 501
Section 11.1Multiple Linear Regression (MLR)Topics-MLRExtension of SLR Statistical model Estimation of the parameters and interpretation R-square with MLR Anova Table F-Test and t-testsA continuation of Chapter 10Most things are conceptually similar
Purdue University - Main Campus - STAT - 501
Section 12.1One-Way Analysis of Variance (ANOVA)Inference for One-Way ANOVAComparing means for several groups Format of data An analogy: two sample t-statistic ANOVA hypotheses and model Understanding two types of variation Estimates of population para
Purdue University - Main Campus - STAT - 501
STAT 501Experimental Statistics IPurpose: To explain the essential ideas and concepts of applied statistics, including numericalsummaries, graphing, hypothesis testing, confidence intervals, two-way tables and the Chi-square,regression and ANOVA. Also
Purdue University - Main Campus - STAT - 501
If you find a mistake, please email me ASAP: colvertn@stat.purdue.edu1.a. 89.248b. 0.2215c. (61.3, 88.7)2.a. 0.0479b. No.c. 0.02563.a. 0.9951b. 0.80304.a.b.c.d.N( = 0.7, = 0.0458)0.1379(0.6084, 0.7916)457 guarantees less than 0.01.5.
Purdue University - Main Campus - STAT - 501
Correlation Exampleoptions ls=72;title1 'Gesell Correlation Example';data gesell;infile 'C:\gesell.txt';input name \$ age score;yrs = age/12; /* creating new variable &quot;yrs&quot; whichconverts age in months to age in years */run;symbol value = circle;p
Purdue University - Main Campus - STAT - 501
Exam 1 Review-Summary of topicsChapter 1 Individuals Categorical and Quantitative variables Graphical tools for categorical variables Bar Chart Pie Chart Graphical tools for quantitative variables Stem and leaf plot Histogram Distributions Describe: Shap
Purdue University - Main Campus - STAT - 501
Test of Mean(s):Hypotheses:One SampleH 0:Ha:Two Sample = 0 &gt; 0 &lt; 0 0H 0:Ha:IF you DO know :X 0nTest of Significance:z=Confidence Interval:X z*n(XX 0snt=1IF you do NOT know :Test of Significance:t=Confidence Interval:X t *sn
Purdue University - Main Campus - STAT - 501
Experiments on learning in animals sometimesmeasure how long it takes a mouse to find itsway through a maze. The mean time is 20seconds for one particular maze. A researcherthinks that playing rap music will cause the miceto complete the maze faster
Purdue University - Main Campus - STAT - 501
Getting Started in SASSome general instructions regarding homeworks:Do not use an alternate program(s) to make any of your graphs, for now just make themby hand, in homework 2 we will start using SAS!Occasionally I will give special instructions for s
Purdue University - Main Campus - STAT - 501
1 Sample t-test in SASoptions nodate pageno=1;goptions colors=(none);title1 'One sample t-test in SAS';data one;infile 'C:\gesell.txt';input name \$ age score;run;proc print data=one;run;One sample t-test in SASObs12345678910111213
Purdue University - Main Campus - STAT - 501
Matched Pairs t-test in SASoptions nodate pageno=1;goptions colors=(none);title 'Analysis of Aggressive behaviors - Example 7.7';data moon;input patient aggmoon aggother;aggdiff = aggmoon - aggother;datalines;1 3.330.272 3.670.593 2.670.324
Purdue University - Main Campus - STAT - 501
2 Sample t-test in SASoptions nodate pageno=1;goptions colors=(none);title1 'DRP data - Example 7.14';data drp;input group score @;datalines;1 24 1 43 1 58 1 71 1 43 1 49 1 61 1 441 67 1 49 1 53 1 56 1 59 1 52 1 62 1 541 57 1 33 1 46 1 43 1 572
Purdue University - Main Campus - STAT - 501
Two-Way Tables in SASoptions nodate pageno=1;goptions colors=(none);title 'Age versus College Program - class example';data one;input age \$ program \$ count;datalines;18below2full3618below2part9818below4full7518below4part3718to212full1
Purdue University - Main Campus - STAT - 502
Stat 502 Topic #2 CLG HandoutActivity #1Data concerning statewide average SAT scores was obtained from www.amstat.org. A complete description ofthe data set may be found at http:/www.amstat.org/publications/jse/datasets/sat.txt . Variables in this data
Purdue University - Main Campus - STAT - 502
Topic 8 Handout: One Way Analysis of VarianceLearning Goals for this Activity: (1) Learn the relationships in the ANOVA table and understand theassociated F test; (2) Understand how to get estimates for cell means model (using the output from SAS); (3)
Purdue University - Main Campus - STAT - 502
Topic 10 Handout: ANCOVA &amp; RCBD DesignsLearning Goals for this Activity: (1) Experience in the use of ANCOVA and RCBD Models; (2) Anunderstanding of why such models are worthwhile.10.1Output for Example II (from notes) is given below on pages 1-2. Com
Purdue University - Main Campus - STAT - 502
Topic 11 Handout: Two Way Analysis of VarianceLearning Goals: (1) Learn how to analyze two factors in ANOVA; (2) Understandand be able to properly interpret interactions.11.1Pages 2 and 3 show six possible interaction plots for an analysis of drugeff
Purdue University - Main Campus - STAT - 502
Topic 12 Handout: CARS exampleLearning Goals: (1) Explore the difference between balanced and unbalanced ANOVAdesigns; (2) Further understanding of interactions; (3) Learn about confounding of effectsin ANOVA.The questions are based on the following s
Purdue University - Main Campus - STAT - 502
Topic 13 Handout: Random EffectsLearning Goals: (1) Understand the differences between fixed effects and random effectsmodels; (2) Be able to identify effects as either fixed or random; (3) Be able to utilize EMS(expected mean squares) to determine (a)
Purdue University - Main Campus - STAT - 502
STAT 502 Assignment #1Coverage: KKMN Chapters 1-3Name: _SCORE: _ of 30Instructions: Although I do encourage you to work together both in and outside of class, remember thatcollaboration on homework problems should be minimal and everyone should creat
Purdue University - Main Campus - STAT - 502
STAT 502 Assignment #1Coverage: KKMN Chapters 1-3Name: _SCORE: _ of 30Instructions: Although I do encourage you to work together both in and outside of class, remember thatcollaboration on homework problems should be minimal and everyone should creat
Purdue University - Main Campus - STAT - 502
STAT 502 Assignment #2Coverage: KKMN Chapters 4-7Name: _SCORE: _ of 40Homework ProblemsThese should be done individually!#1.(3 pts) Briefly explain the difference between the following two equations. Do either of theseconstitute a complete statemen
Purdue University - Main Campus - STAT - 502
STAT 502 Assignment #3Coverage: KKMN Chapter 8-9Name: _SCORE: _ of 40Homework ProblemsThese should be done individually!Please note that HW problems generally do not require any SAS coding.#1.(6 points) KKMN Problem 8.03 as stated. Please note that
Purdue University - Main Campus - STAT - 502
STAT 502 Assignment #4Coverage: KKMN Chapter 9Name: _SCORE: _ of 40Homework ProblemsThese should be done individually!Please note that HW problems generally do not require SAS coding.#1.(6 points) KKMN Problem 9.02.#2.(4 points) KKMN Problem 9.03
Purdue University - Main Campus - STAT - 502
STAT 502 Assignment #5Coverage: KKMN Chapters 10 &amp; 12Name: _SCORE: _ of 40Homework ProblemsThese should be done individually!Please note that HW problems generally do not require SAS coding.#1.(7 points) KKMN Problem 10.07. Ignore the questions in
Purdue University - Main Campus - STAT - 502
Topic 1 Basic StatisticsKKMN Chapters 1-31Topic OverviewCourse Syllabus &amp; ScheduleReview: Basic StatisticsTerminology: Being able to CommunicateDistributions: Normal, T, FHypothesis Testing &amp; Confidence IntervalsSignificance Level &amp; Power2Textb
Purdue University - Main Campus - STAT - 502
Topic 2 Simple Linear RegressionKKMN Chapters 4 71OverviewRegression Models; Scatter PlotsEstimation and Inference in SLRSAS GPLOT ProcedureSAS REG ProcedureANOVA Table &amp; Coefficient ofDetermination (R2)2Simple Linear Regression ModelWe take n
Purdue University - Main Campus - STAT - 502
CLG Activity #1Please discuss questions 3.1-3.6from the handout.CLG Activity #1Q1: Research Questions?Is there an effect of smoking on SBP?Is body size associated to SBP?Can any combination of the three variablesbe used to predict SBP?CLG Activit
Purdue University - Main Campus - STAT - 502
Topic 3 Multiple Regression AnalysisRegression on Several PredictorVariables(Chapter 8)1Topic OverviewSystolic Blood Pressure ExampleMultiple Regression ModelsSAS Output for RegressionMulticollinearity2Systolic Blood Pressure DataIn this topic
Purdue University - Main Campus - STAT - 502
Topic 4 CLG Addendum1CLG Activity #1In your groups, please attempt thefirst set of questions. These willinvolve computing various extrasums of squares.2Question 4.1 &amp; 4.2Univariate and bivariate issues that mayaffect modeling include:For HSM, H
Purdue University - Main Campus - STAT - 502
Topic 4 Extra Sums of Squaresand the General Linear TestUsing Partial F Tests in MultipleRegression Analysis(Chapter 9)1Recall: Types of Tests1.ANOVA F Test: Does the group of predictorvariables explain a significant percentage of thevariation i
Purdue University - Main Campus - STAT - 502
CLG ActivityIn CLGs, please attempt Activity#1 from the handout for Topic 5.Note that this activity builds on theone we used for Topic #4.15.1 (a) &amp; (b)2GPA, HSM | HSS , HSE , SATM , SATVr2GPA , HSE | HSMr6.835== 0.061105.65 + 6.8352.48=
Purdue University - Main Campus - STAT - 502
Topic 5 Partial Correlations; Diagnostics &amp;Remedial MeasuresChapters 10 &amp; 141OverviewReview: MLR Tests &amp; Extra SSPartial Correlations Think Extra SS beingused to compute Extra R2Of the variation left to explain.How much isexplained by adding anot
Purdue University - Main Campus - STAT - 502
Topic 6 Model SelectionSelecting the BestRegression Model(Chapters 9 &amp; 16)1OverviewWe already have many of the pieces inplace. Well use those to developalgorithmic procedures.There are some additional statistics that canbe used for comparison of
Purdue University - Main Campus - STAT - 502
Topic 7 Other Regression IssuesReading: Some parts ofChapters 11 and 15OverviewConfounding (Chapter 11)Interaction (Chapter 11)Using Polynomial Terms (Chapter 15)Regression: Primary GoalsWe usually are focused on one of thefollowing goals:Predic
Purdue University - Main Campus - STAT - 502
Topic 8 One-Way ANOVASingle Factor Analysis of VarianceReading: 17.1, 17.2, &amp; 17.5Skim: 12.3, 17.3, 17.41OverviewNote: Entire topic constitutes some reviewas this would be the last thing you coveredin 501. We will cover it perhaps insomewhat more
Purdue University - Main Campus - STAT - 502
Topic 8 One-Way ANOVASingle Factor Analysis of VarianceReading: 17.1, 17.2, &amp; 17.5Skim: 12.3, 17.3, 17.41OverviewNote: Entire topic constitutes some reviewas this would be the last thing you coveredin 501. We will cover it perhaps insomewhat more
Purdue University - Main Campus - STAT - 502
Topic 9 Multiple ComparisonsMultiple Comparisonsof Treatment MeansReading: 17.7-17.81OverviewBrief Review of One-Way ANOVAPairwise Comparisons of Treatment MeansMultiplicity of TestingLinear Combinations &amp; Contrasts ofTreatment Means2Review: O
Purdue University - Main Campus - STAT - 502
Topic 10 ANCOVA &amp; RCBDAnalysis of Covariance (Ch. 13)Randomized Complete BlockDesigns (Ch. 18)1ReviewRecall the idea of confounding. Suppose I want todraw inference about a certain predictor.If meaningfully different interpretations would bemade
Purdue University - Main Campus - STAT - 502
Topic 11 ANOVA IIBalanced Two-Way ANOVA(Chapter 19)1Two Way ANOVAWe are now interested the combined effectsof two factors, A and B, on a response (note:text refers to these as R = rows andC = columns well call them A, B, and laterC for a 3-way AN
Purdue University - Main Campus - STAT - 502
Topic 12 Further Topics in ANOVAUnequal Cell Sizes(Chapter 20)1OverviewWell start with the Learning Activity.More practice in interpreting ANOVA results; anda baby-step into 3-way ANOVA.An illustration of the problems that anunbalanced design wil
Purdue University - Main Campus - STAT - 502
Topic 13 Random EffectsBackground Reading:Parts of Chapters 17 and 191Reading SummarySection 17.1 (particularly page 422)Section 17.6 (pages 438-440)Section 19.7 (pages 538-541)2Random EffectsSo far we have really only dealt with fixedeffects w
Purdue University - Main Campus - STAT - 502
Topic 14 Experimental DesignCrossoverNested FactorsRepeated Measures1OverviewWe will conclude the course by consideringsome different topics that can arise in amulti-way ANOVA, as well as some othermiscellaneous topics.Some of these are discusse
Purdue University - Main Campus - STAT - 506
STAT 506Homework 1You should first go the the website and download the Data folder for the Programming 1course, it is available in a zip file called prg1.zip. I suggest you use your H: drive for storagebut its really up to you. You will need to unzip i
Purdue University - Main Campus - STAT - 506
STAT 506Homework 2For most problems you will still need to access the data in the PRG1 folder. Use the libname statement we learned toload this each time you work on your assignments. You may now call it orion to be consistent with the SASmaterials. Th