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# STATISTICAL METHODS STAT 303

Texas A&M

GPA 3.5

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This 14 page Class Notes was uploaded by Celestino Bergnaum on Wednesday October 21, 2015. The Class Notes belongs to STAT 303 at Texas A&M University taught by Staff in Fall. Since its upload, it has received 73 views. For similar materials see /class/225758/stat-303-texas-a-m-university in Statistics at Texas A&M University.

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Date Created: 10/21/15

1 The distribution ofvalues of a statistic in all possible samples ofthe same size from the same population is known as 2 Twenty multiplechoice questions are on an exam each having responses a b c d or e Suppose a student guesses the answer to each question and the guesses from question to question are independent Let X be the number of questions for which the student has the same answer as the person sitting next to him on his right The distribution ofX is Binomial 3 A random sample of size 25 is to be taken from a population that is normally distributed with mean 60 and standard deviation 10 The average Yof the observations in our sample is to be computed The sampling distribution of Y is 4 I take a SRS of size n from a population that has mean u 80 and standard deviation 0 20 How big should n be so that the sampling distribution of Yhas standard deviation 07 1 5 Suppose we select an SRS of size n100 from a large population having proportion p of successes Let X be the number of successes in the sample For which value of p would it be safe to assume the sampling distribution ofX is approximately normal B 19 C 0975 D 09999 E More than one ofthe above is correct 6 A college basketball player makes 80 of his free throws Over the course of the season he will attempt 100 free throws Assuming freethrow attempts are independent what is the probability that he makes at least 90 of these attempts 7 Suppose we have a random sample size n 30 from N5 J52 What is the chance that 7c is less than 54 8 For which ofthe following does it make sense to talk about a sampling distribution A Sample mean B Sample variance C Population mean D Two ofthe above 9 The SAT scores of entering freshman at University Y are N1215 1102 A random sample of 100 freshman is sampled with Ybeing the sample mean of the 100 scores from University Y The probability that 17 is less than 1190 is 10 The blood cholesterol of a large population of adult males 50 60 years old is distributed with a mean of 200 mgdl with a standard deviation of 20 mgdl Assume that blood cholesterol measurements are normally distributed What is the probability that a randomly selected individual from this age group will have a blood cholesterol level below 250 mgdl 11 Using information from the previous problem what is the probability that the mean of a sample of 100 men from this age group will have a value below 250 mgdl 12 lffa N3022 what is the probability that f7 gt33 6293 9332 3707 0668 5000 r099 Keys l A A O 7 8 Sampling distribution B202 N6022 n400 B 00062 09394 D 9 00116 10 09938 11 1 12D A restaurant owner is interested in knowing what the average age is of his customers He takes a random sample of 30 people who visit the restaurant and records their age The ages are as follows 24 10 27 9 20 43 32 47 38 4819 3617 3 40 ll 31 42 33 39 7 41 l 8 44 46 50 35 26 45 Suppose the true average age is 28 with a standard deviation of 32 What is the approximate sampling distribution of the sample mean 5 87230 2907 2 2 7 o 7 32 7 2 MN 7 7N287 7N280584 x y 42 J E 430 J Where did our sample mean fall in the sampling distribution Z 2907728 0178 32 Ans 0178 standard deviations above the true mean ON YOUR OWN A study was conducted to see how often Texas AampM students talk on their cell phones A random sample of 30 students was taken and the number of phone calls each student made that day was recorded The results were 3 8 14 ll 9 6 15 201910l2l5 5 2 14 10 l 4 8 3 ll 18 4 14 710 2 l3 6 8 Suppose the true average was 123 with a standard deviation of 26 What is the approximate sampling distribution Where did our sample fall in the sampling distribution Answers N1 23 0475 2 Our sample mean fell 112 standard deviations below the mean Test 3 Review What material will be covered on this exam Chapter 71 72 and Chapter 8 will be covered on the exam How should I study for this exam 0 Read the chapters and slides o Redo the assigned homework and look at solutions 0 Rework the review problems I did in class 0 Review your lab exercise and handouts 0 Work through some old exams 0 Make a formulanotes sheet to bring with you suggest one side of it as Hypothesis testing flow chart can write corresponding confidence interval formulae on it What can I bring with me to the exam 0 85 x 11 notes sheet with anything you want on it except no photocopies of anything 0 Gray 85 x 11 scantron o Calculator 0 Ztable and Ttable will be provided 0 Pencil and Erasers 0 Picture ID Ch 0 Test 3 Review apter 7 One sample tstatistic and its degrees of freedom When to use one sample tstatistic Know how to read ttable how it is different from ztable how to find probabilities gt lt not Confidence Interval for 1 samplet Hypothesis testing for 1 sample t Matched pairst paired t When to use matched pairs Confidence interval for matched pairs Hypothesis testing for matched pairs Know that matched pairs is more powerful than a 2 sample ttest Two sample problems Two sample zstatistic When to use a two sample zstatistic Two sample tstatistic and its degrees of freedom When to use a two samplet Confidence Interval for two sample t Hypothesis testing for two sample t Two sample pooled ttest we use this when 0102 Two sample pooled t Confidence Interval Test 3 Review CHAPTER 8 Section 81 Confidence Interval for a Population Proportion Using largesample method instead of the Wilson method LargeSample Significance Test for a Population Proportion Sample Size for a Desired Margin of Error Know Definitions Definition and Interpretation of Confidence Intervals Common Confidence Levels and the associated 2 value Relationship between width of interval confidence level and risk of being incorrect Find Confidence Intervals for Proportions largesample and Assumptions for each formula Given Confidence Interval ie21t5412 find confidence level n or 0 Ways to reduce your margin of error Sample Size Calculations Setting up Hypothesis Testing Steps 1 amp 2 dSignificance Level Interpretation Step 3 Finding Test Statistics Step 4 Finding Pvalues Step 5 Given pvalues decision rule Conclusions Steps 6 and 7 Difference between onesided and twosided tests Relationship between Confidence Intervals and twosided Hypothesis Testing Find Confidence Intervals for Proportions Given Confidence Interval find confidence level Sample Size Calculations Normality Assumptions Section 82 o Zstatistic for 2 proportions 0 When to use 2 sample Z for proportions 0 Confidence intervals for 2 proportions o Hypothesis testing for 2 proportions pooled proportion Test 3 Review Julie s Review 1 2 What to Know for the Test sample t test sample t test pooled t test 2 sample proportions Know when to do which test Also know for each P FnPSJ N NP WPPNEO Ho and HE Type and Type II errors necessary assumptions write them on the flowchart range of the p value for t tests given p value what s the conclusion in the words of the problem given 3 Cl s what s the range of the p value eneral info add Cl formulas to the flowchart interpretation of Cl s power and what affects it know which df s for 1sample t tests and df s for the 2sample t test difference and similarities of the Z and tcurves why we use a tand not a Z which t test has the most power paired gt pooled gt 2sample 2 1sample Test 1 Review Exam 1 Review How should I study for this exam Read the chapters 13 and section 91 Review the homework with the solutions Rework the review problems I did in class Work through my old exam Make a formulanotes sheet to bring with you What to bring with you to the exam One 85 x 11 notes sheet with anything you want to print or type No Xeroxing anythingfriends formula sheet notes old exams etc Gray 85 x 11 Scantron Calculator Pencil and Eraser Picture ID Chapter 1 Individual Variables Categorical vs Quantitative Numeric Graphically Summarizing Data Bene ts of one over another Frequency Tables counts or percents Bar Graphs counts or percents Pie Charts counts or percents StemandLeaf Plots how to construct how to read how to describe using shape symmetry leftskewed right skewed center and spread find IQR find 5 number summary etc number of modes outliers Histogram counts or relative frequencies how to construct how to read how to describe using shape symmetry leftskewed right skewed center and spread nd IQR nd 5 number summary etc relationship between mean and median number of modes outliers given counts get relative frequencies or given relative frequencies find counts How to describe a distribution using shape center and spread Skewness How does it affect the mean and median Mean how to compute measurement of center when to use when describing center Median how to compute given even and odd datasets measurement of center when to use when describing center Quantiles how to find given data or graphical summary Boxplots Identify 5 number summary symmetry vs skewness spread of data determining outliers ltQ115QR or gtQ315QR IQR Compute how to use it to designate outliers Test 1 Review Variance interpretation Standard Deviation Not have to compute interpretation given sets of numbers which has largestsmallest s properties Choosing a measure of center and spread know when to use meanmedian to describe center and when to use standard deviationIQR to describe spread etc Shift amp Scale changes and its effects on descriptive statistics Linear Transformations Given a graphical summary of data nd a second graphically summary that matches the rst Ex Which boxplot matches the given histogram which histogram matches the given boxplot which stemandleaf plot matches the given histogram which boxplots matches the given stemandleaf plot etc Density Curves properties mean and median of density curve quartiles Area under curve equals 1 Relative frequency area under curve probability Standard Normal Distribution properties Find PrZlt PrZgt PrltZlt PrZlt or Zgt given like this or in situational context Find PrZltz PrZgtz Prz1ltZlt22 PrZlt 21 or Zgt 22 given like this or in situational context Normal Distributions Empirical Rule 6895997 Rule Standardizing z x 039 notation Nuo2 Find PrXlt PrXgt PrltXlt PrXlt or Xgt given like this or in situational context Find PrXltx PrXgtx Prx1ltXltx2 PrXlt x1 or Xgt x2 given like this or in situational context Normal Quantile QQ Plots how to interpret outliers Test 1 Review Chapter 2 Association between variables positive or negative Response Variable How to identify it in a situation dependent Explanatory Variable How to identify it in a situation independent Scatterplots which variable goes on each axis interpretation overall pattern form direction strength outliers positive association negative association Correlation Not have to compute what does it measure interpretation properties direction strength outlier Least Squares Regression Regression Line outliers in xy direction required variables equation interpretation of slope and intercept general idea of how to fit the least squares regression line predictive abilities Correlation and Regression R2 de nition interpretation Lurking Variables Outliers and In uential Observation de nitions how do they affect the regression line and correlation Association vs causation Establishing Causation Confounding Variables SKIP SECTION 26 Chapter 9 Section 91 Two Way Tables counts and percents Row Variable Column Variable Cell Simpson s Paradox Find proportions using tables with and without rowcolumn totals and with either counts or proportions Conditional Probabilities Test 1 Review CHAPTER 3 Section 31 Exploratory data analysis Designs Sample Population Census Observational Study Experiment evidence for causation Section 32 Experimental Units Subjects Treatment Placeboplacebo effect Control Group Bias Randomization How to randomize how to use a table of random digits Doubleblind Section 33 Population Sample Voluntary Response Sample Simple Random Samples Stratified Random Sample Cluster Sampling Multistage samples Wording of questions Section 34 Statistical Inference Sampling Variability Sampling Distributions Bias and Variability Managing Bias and Variability how to reduce Test 1 Review Know Definitions How to define the population of interest AdvantagesDisadvantages of taking a census vs a survey Idea of Inferential Statistics Ideas of bias and independence Given a situation be able to distinguish if it is a SRSStratifiedCIusterMultistageetc Know how to use a Random Number Table to select sample Sampling Problems Concepts of Confounding Variables and Interaction Experiment vs Observational Study Parameter vs Statistic What is a sampling distribution Difference between Bias and Variability and how to improve them

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