Stat 321 – Lecture 28Quiz 7AnnouncementsQuick OverviewChapter 5Slide 6Chapter 6Chapter 7Quiz/Lab/Exam FeedbackFinal ExamAdvice?GameThanks…Slide 14Stat 321 – Lecture 28ReviewLast piece of advice:Keep in mind that 17% of statistics are made up on the spot.Quiz 7Wanted to show E( 2) ≠ 2E(X2) ≠ [E(X)]2Needed another way of finding E(X2)V(X) = E(X2) – [E(X)]2 but here know variance and expected value of the sample mean!XAnnouncementsLocation of finalCurrent course grade in BBReflects through HW 8 including one drop, Lab 6, Quiz 6 including 2 dropsQuick OverviewPopulationSampleProbabilityStatisticsWhat does “probability” mean?How do we calculate probabilities for different kinds of events?What are the common models?Describing a distribution of data/important summary featuresMaking inferences from data to the population/process (when valid?)Chapter 5Sampling DistributionsTo know what conclusions we can make from a sample statistic, we need to know about the “precision” and behavior of the sample statistic in many samplesThis allows us to assess where we think the population parameter might be/whether we have a surprising outcome for a particular conjecture about the populationChapter 5Sampling DistributionsDescribe shape, center, spreadIf possible, list out all possible samplesOtherwise, does the Central Limit Theorem apply?Means, Sums, Proportions (Binomial)Be able to calculate probabilities (e.g., Quiz 6)If notConsider using rules of expectation and variance (linear combinations)Consider simulating an empirical sampling distributionKnow how impacted by changes (e.g., n)Chapter 6Properties of estimatorsUnbiased?Finding expected value of discrete/continuous random variablesRules for expectation (linear functions, V(X) shortcut)Finding the formula for the variance using rules of varianceEvaluating simulation resultsDeriving an estimatorMethod of MomentsMaximum likelihoodChapter 7Confidence intervalsGeneral principleWhat “confidence” means (how relates to probability)Selecting which confidence interval formula to useJustifications behind the methodsInterpreting, making inferences based on intervalHow impacted by changes (e.g., n)Solving for desired sample sizePrediction interval for individual observationQuiz/Lab/Exam FeedbackBe careful with notation, know how to label graphs, calculationsWhat’s a number? What’s a random variable?Know the interpretation/principles behind the calculationsWork problems!Get something written down…Show workEmail questionsFinal ExamFormulas and tables provided (see formulas pages online)3 notes pages of your ownEmphasis on Ch. 5-7 but cumulative1/3, 1/3, 1/3See problem solving strategies onlineAdvice?Be prepared to think/explain/interpret Do not just plug into formulas from text Understand, don’t memorize Organize notes for efficient retrieval of information Re-read Handouts, especially expository passages, “boxed” paragraphs Review sheets from first two exams Solutions from first two exams Chapters from text Review problems Re-work examples from handouts Re-work homework problems Re-work examples from text Re-work questions from previous exams Work additional exercises from textGameRandom variable or number? S2sE(p-hat)X1+X2V(X1 +
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