Midterm ReviewFall 2011BasicsTime and place (usual): 331 SMI 11:00 AM - 12:15 PMBring a Calculator. NO laptop, NO cell phones (NO otherelectronic devices).Coverage: Everything through Chapter 6 including thenotes on simulation experiments.Closed notes, closed book.Formula sheet 812× 11 sheet (both sides).Other Questions?Practice ProblemsLook at the HW ProblemsLook at the HW Solutions - gives ideal for getting partialcredit.Examples covered in lecture notes.Examples in your textbook - e.g. p.103 Example 3.44.Gives a good practice problem for the Binomial distribution.Tables to KnowStandard Normal Distribution - Table 3 (p.675-676).t Distribution - Table 4 (p. 677).Warning!I highlight some of the main topics below.Of course you are responsible for everything covered inlecture and HW assignments.Populations and SamplesWhat is the target populationIs the sample truly a random sample from the populationIs the sample representativeExploratory data analysisDistinguish categorical/numerical data,Display distributions, describe their shape,Boxplots: determine Q1, median, Q3, detect outliers,Calculate the mean and standard deviation(don’t forget to√var !)Discrete Random VariablesFormula for the mean and variance.Be able to compute questions given a probability tableStandard ProblemConsider a random variable X defined by the followingdistributionk 0 1 5 10P(X = k) 0.1 0.5 0.1 0.31Compute P(X ≥ 5)2Compute P(.5 ≤ X ≤ 6)3Compute E(X), Var(X), and SD(X)Binomial distributionGiven the description of a random variable Y, determinewhether it has a binomial distribution or not. If informationis available, give n and p.The BInS assumption p.104-105 (See p.110 Example 3.50)Know the mean and variance formulas for the Binomial.Carry out probability calculations with BKnow how to approximate B with N (possibility of thecontinuity correction).Normal distributionCarry out probability calculations: IP{Y ≤ a} =?,IP{Y ≥ a} =?, IP{a ≤ Y ≤ b} =?,and quantile calculations: IP{Y ≤?} = p, IP{Y ≥?} = p.Use the transformation Z =Y−µσSampling Distribution ofˆpKnow the expected value and variance.Also, see related questions from HWSampling Distribution of¯Yif Y1, . . . , Ynhave mean µ and standard deviation σ, then¯Yhas mean µ, standard deviation σ/√n.¯Y ∼ N if Y1, . . . , Yn∼ N.In any case,¯Y still ∼ N when n is large.Confidence Intervals - one sampleConstruct and interpret a confidence interval for apopulation mean.Construct and interpret a confidence interval for apopulation proportion.Determine a sample size necessary to achieve a givenprecision.Remember interpret.Confidence Interval for a Population Mean¯y ± tSE¯y,SE¯y=s√nInterpretation ExampleConclusionWe are 95% confident that the average daily milk yield of a cowin the herd the cows were sampled from is between 30.6 and41.8 lbs.Confidence intervals for proportions˜p =y + 2n + 4and SE˜p=r˜p(1 −˜p)n + 4A 95% confidence interval for p is˜p ± 1.96
View Full Document
Unlocking...