Sociology 301. Sampling Distribution and Central Limit Theory. Sampling Distribution. Inferential Statistics. We want to draw conclusions about
|
|
- Ernest Flowers
- 5 years ago
- Views:
Transcription
1 Sociology 30 and Central Limit Theory Liying Luo Schlitz vs. Michelob Super Bowl XV Commercial Why was Schlitz so sure that the results aired live at Super Bowl halftime would not screw them? Inferential Statistics We actually observe a Sample of cases a Population of Cases We want to draw conclusions about a Sample of cases Descriptive Statistics (Why would we do this?) a Population of Cases Inferential Statistics Descriptive Statistics
2 Inferential Statistics Popula(on Parameter: numeric afributes of a populagon Sample Sta(s(cs: numeric afributes of a sample a populagon parameter or sample stagsgcs: Mode of the SEXFREQ in the GSS? Standard deviagon of the height of the students in the room? Average age in the 200 Census data? Inferential Statistics In the Schlitz vs Michelob example Population? Population parameter? Sample? Sample statistics? Inferential Statistics A CNN/ORC poll conducted a poll among 248 registered voters who described themselves as republicans on March Candidate Percentage Trump 47% Cruz 3% KaGch 7% Someone else 3% None/no one % No opinion % In this example Population? Population parameter? Sample? Sample statistics?
3 Recall the definigon distribugon... Consider taking one random sample consisgng of 5 students from a class and calculagng the proporgon of preferring Pepsi in the sample. Then take another random sample consisgng of 5 students from the same class and calculate the proporgon of preferring Pepsi. Would you expect both proporgons to be exactly the same? The distribugon of a sample stagsgc has a special name Sampling Distribu(on: the distribugon of sample stagsgcs (CLT): If n (sample size) is sufficiently large, then the sample means from many random samples from a populagon with mean μ and variance σ 2 are approximately normally distributed with mean μ and variance σ 2 /n regardless of the distribugon of the original variable. Sampling distribu(on vs sample distribu(on
4 Sample Distribution Draw a random sample of 50 college students and record Sociology majors. What does the distribugon of these 50 observagons look like? Draw a random sample of 0 college students and record their GPA. What does the distribugon of these 0 GPAs look like? Sample Distribution Sample distribugon: distribugon of observagons in one sample Random Sample Random Sample of n=0 college students No Sociology Major? es Sample Distribution Sample distribugon: distribugon of observagons in one sample Random Sample Random Sample of n=0 college students No Sociology Major? es Sample Percentage = 4.0% Sample Mean = 3.0
5 Draw a random sample of 50 college students and calculate the proporgon of Sociology majors. Repeat the process,000 Gmes. What does the distribugon of the,000 proporgons look like? Draw a random sample of 0 college students and calculate their average GPA. Repeat the process 0,000 Gmes. What does the distribugon of the 0,000 average GPAs look like? Random Sample Random Sample of n=0 college students Sample Percentage = 4.0% Sample Mean = 3.0 0% 4% 8% 2% 6% 20% 24% 28% 32% of n=0 college students 0% 4% 8% 2% 6% 20% 24% 28% 32%
6 20 20 of n=0 college students 0% 4% 8% 2% 6% 20% 24% 28% 32% of n=0 college students 0% 4% 8% 2% 6% 20% 24% 28% 32% ,000,000 of n=0 college students 0% 4% 8% 2% 6% 20% 24% 28% 32%
7 00,000 00,000 of n=0 college students 0% 4% 8% 2% 6% 20% 24% 28% 32% Infinity Infinity of n=0 college students 0% 4% 8% 2% 6% 20% 24% 28% 32% (CLT): If n is sufficiently large, then the sample means from many random samples from a populagon with mean μ and variance σ 2 are approximately normally distributed with mean μ and variance σ 2 /n regardless of the distribugon of the original variable.
8 From the 880 Census, the population distributions of Born in the United States? Number of People in the Household True Population Mean µ = 5.3 True Population Proportion p = Number of People in the Household Born in the US? (0=No, =es). I sampled 00 individuals (n=00), and computed the sample proporgon born in the U.S. the sample mean number of people in the household 2. I repeated that procedure 999 more Gmes. sample distribution of # of people sampling distribution of average # of people # of people in the household
9 Binomial Random Variables Binomial Random Variables For binomial random variable based on n trials with probability of success on any given trial equal to p, the For binomial expected random value of variable (or µ ) equals based on n trials with probability E() of = success μ = np on any given trial equal to p, the expected value sample of (or distribution µ of sampling distribution of the variance σ 2 birth equals ) equals place proportion of native-born E() = μ σ 2 =np( = np -p) the variance σ 2 equals Born in the US? and the standard deviation σ equals σ 2 =np( -p) 2 σ = σ = np( -p) and the standard deviation σ equals 2 σ = σ = np( -p) Binomial Random Variables Binomial Random Variables Because a binomial random variable is just a special case of discrete random variables, the formula used to compute Because Central the mean a Limit binomial Theorem and variance random (CLT): of variable Using a discrete sample is just random a stagsgcs special variable to case esgmate of populagon parameters. discrete random variables, k the formula used to compute the mean E() and = μ variance = p( ) i i i= of a discrete random variable : sample k mean 2 2 k σ = ( μ p() i i se E() : standard = μ = i p error; ( ) i i standard deviagon of the sample mean. i= k 2 will 2 also work for binomial random variables (if you are inclined to σ = ( μ ) p() i i do i= extra math) will also work for binomial random variables (if you are inclined to do extra math) Binomial Random Variables Binomial Random Variables Whether a newborn baby is a boy is a binomial experiment with p = 0.52 Whether Central For the a newborn Limit binomial baby Theorem random is a boy variable is a binomial number experiment of boys based with on p = n 0.52 = 00 randomly selected births: For the E() binomial = μ = np 00x random = variable = number of boys based on When n = 00 σthe 2 = randomly populagon np(-p) = selected 00(0.52)( standard births: deviagon 0.52) is = known E() = s se σμ 2 = = np σ = 00x np(-p) 0.52= = = σ 2 = np(-p) n = 00(0.52)( 0.52) = If we sampled 00 births and counted the number of boys 2 σ : = standard σ then = np(-p) deviagon repeated = of that the experiment populagon = an infinite number of If we n times we sampled : size 00 would births average and counted 5.2 boys the with number σ = of boys and then repeated that experiment an infinite number of times we would average 5.2 boys with σ = Sociology 38 ~ February 0, Sociology 38 ~ February 0, Sample Estimate ± ± t a/2 s n
10 Recap Probability: How likely a pargcular outcome of an event will occur Normal Distribu(on: Z-Score: the number of standard deviagons an observagon is above or below the mean. i Zi s Recap μ 6 6 ou select one sample of n = 0 college students. What is the probability that your sample mean GPA differs from the populagon mean by more than ±0.4? μ Infinity of n=0 college students for Mean GPA µ = 3.0 σ = 0.2
11 Born in the United States? Worksheet 95% of the chance that the sample mean will fall within.96 standard deviagons of the populagon mean. ou select one sample of n=0 college students 6 6 Infinity of n=0 college students μ What is the probability that your sample mean GPA ( x ) differs from the population mean by more than ±0.4? for Mean GPA µ = 3.0 σ = 0.2 Worksheet ou select one sample of n=0distribution college students Sampling and Infinity your sample mean GPA ( x ) is greater than 3.5? of n=0 college students is the probability SchlitzWhat vs. Michelob Super Bowlthat XV Commercial for Mean GPA µ = 3.0 σ = 0.2 Soc 38-2/7/205 Worksheet 00 Michelob drinkers were randomly selected to conduct a blind taste test between Michelob and Schlitz. Why was Schlitz so sure that the results aired live at Super Bowl haloime would not screw them? 6
12 Exercise ou selected one random sample of,000 people and got a sample mean of 5 for the outcome of interest. It is known that standard deviagon of the populagon 20. What is the probability that your sample mean differs from populagon mean by more than 5?
Chapter 7 presents the beginning of inferential statistics. The two major activities of inferential statistics are
Chapter 7 presents the beginning of inferential statistics. Concept: Inferential Statistics The two major activities of inferential statistics are 1 to use sample data to estimate values of population
More informationMidterm Exam III Review
Midterm Exam III Review Dr. Joseph Brennan Math 148, BU Dr. Joseph Brennan (Math 148, BU) Midterm Exam III Review 1 / 25 Permutations and Combinations ORDER In order to count the number of possible ways
More informationECO220Y Estimation: Confidence Interval Estimator for Sample Proportions Readings: Chapter 11 (skip 11.5)
ECO220Y Estimation: Confidence Interval Estimator for Sample Proportions Readings: Chapter 11 (skip 11.5) Fall 2011 Lecture 10 (Fall 2011) Estimation Lecture 10 1 / 23 Review: Sampling Distributions Sample
More informationChapter 4 Probability Distributions
Slide 1 Chapter 4 Probability Distributions Slide 2 4-1 Overview 4-2 Random Variables 4-3 Binomial Probability Distributions 4-4 Mean, Variance, and Standard Deviation for the Binomial Distribution 4-5
More informationChapter 5. Sampling Distributions
Lecture notes, Lang Wu, UBC 1 Chapter 5. Sampling Distributions 5.1. Introduction In statistical inference, we attempt to estimate an unknown population characteristic, such as the population mean, µ,
More informationMidterm Test 1 (Sample) Student Name (PRINT):... Student Signature:... Use pencil, so that you can erase and rewrite if necessary.
MA 180/418 Midterm Test 1 (Sample) Student Name (PRINT):............................................. Student Signature:................................................... Use pencil, so that you can erase
More informationNo, because np = 100(0.02) = 2. The value of np must be greater than or equal to 5 to use the normal approximation.
1) If n 100 and p 0.02 in a binomial experiment, does this satisfy the rule for a normal approximation? Why or why not? No, because np 100(0.02) 2. The value of np must be greater than or equal to 5 to
More informationChapter 9 & 10. Multiple Choice.
Chapter 9 & 10 Review Name Multiple Choice. 1. An agricultural researcher plants 25 plots with a new variety of corn. The average yield for these plots is X = 150 bushels per acre. Assume that the yield
More information7. For the table that follows, answer the following questions: x y 1-1/4 2-1/2 3-3/4 4
7. For the table that follows, answer the following questions: x y 1-1/4 2-1/2 3-3/4 4 - Would the correlation between x and y in the table above be positive or negative? The correlation is negative. -
More informationOverview. Definitions. Definitions. Graphs. Chapter 4 Probability Distributions. probability distributions
Chapter 4 Probability Distributions 4-1 Overview 4-2 Random Variables 4-3 Binomial Probability Distributions 4-4 Mean, Variance, and Standard Deviation for the Binomial Distribution 4-5 The Poisson Distribution
More informationAMS7: WEEK 4. CLASS 3
AMS7: WEEK 4. CLASS 3 Sampling distributions and estimators. Central Limit Theorem Normal Approximation to the Binomial Distribution Friday April 24th, 2015 Sampling distributions and estimators REMEMBER:
More informationThe normal distribution is a theoretical model derived mathematically and not empirically.
Sociology 541 The Normal Distribution Probability and An Introduction to Inferential Statistics Normal Approximation The normal distribution is a theoretical model derived mathematically and not empirically.
More informationThe Central Limit Theorem. Sec. 8.2: The Random Variable. it s Distribution. it s Distribution
The Central Limit Theorem Sec. 8.1: The Random Variable it s Distribution Sec. 8.2: The Random Variable it s Distribution X p and and How Should You Think of a Random Variable? Imagine a bag with numbers
More informationMA131 Lecture 9.1. = µ = 25 and σ X P ( 90 < X < 100 ) = = /// σ X
The Central Limit Theorem (CLT): As the sample size n increases, the shape of the distribution of the sample means taken with replacement from the population with mean µ and standard deviation σ will approach
More informationStatistics, Their Distributions, and the Central Limit Theorem
Statistics, Their Distributions, and the Central Limit Theorem MATH 3342 Sections 5.3 and 5.4 Sample Means Suppose you sample from a popula0on 10 0mes. You record the following sample means: 10.1 9.5 9.6
More informationBinomial and Normal Distributions
Binomial and Normal Distributions Bernoulli Trials A Bernoulli trial is a random experiment with 2 special properties: The result of a Bernoulli trial is binary. Examples: Heads vs. Tails, Healthy vs.
More informationBinomial Distributions
Binomial Distributions Binomial Experiment The experiment is repeated for a fixed number of trials, where each trial is independent of the other trials There are only two possible outcomes of interest
More informationSAMPLING DISTRIBUTIONS. Chapter 7
SAMPLING DISTRIBUTIONS Chapter 7 7.1 How Likely Are the Possible Values of a Statistic? The Sampling Distribution Statistic and Parameter Statistic numerical summary of sample data: p-hat or xbar Parameter
More informationThe Central Limit Theorem
Section 6-5 The Central Limit Theorem I. Sampling Distribution of Sample Mean ( ) Eample 1: Population Distribution Table 2 4 6 8 P() 1/4 1/4 1/4 1/4 μ (a) Find the population mean and population standard
More informationUsing the Central Limit Theorem It is important for you to understand when to use the CLT. If you are being asked to find the probability of the
Using the Central Limit Theorem It is important for you to understand when to use the CLT. If you are being asked to find the probability of the mean, use the CLT for the mean. If you are being asked to
More informationMath : Spring 2008
Math 1070-2: Spring 2008 Lecture 7 Davar Khoshnevisan Department of Mathematics University of Utah http://www.math.utah.edu/ davar February 27, 2008 An example A WHO study of health: In Canada, the systolic
More informationReview. Preview This chapter presents the beginning of inferential statistics. October 25, S7.1 2_3 Estimating a Population Proportion
MAT 155 Statistical Analysis Dr. Claude Moore Cape Fear Community College Chapter 7 Estimates and Sample Sizes 7 1 Review and Preview 7 2 Estimating a Population Proportion 7 3 Estimating a Population
More informationMLLunsford 1. Activity: Central Limit Theorem Theory and Computations
MLLunsford 1 Activity: Central Limit Theorem Theory and Computations Concepts: The Central Limit Theorem; computations using the Central Limit Theorem. Prerequisites: The student should be familiar with
More informationLECTURE 6 DISTRIBUTIONS
LECTURE 6 DISTRIBUTIONS OVERVIEW Uniform Distribution Normal Distribution Random Variables Continuous Distributions MOST OF THE SLIDES ADOPTED FROM OPENINTRO STATS BOOK. NORMAL DISTRIBUTION Unimodal and
More informationReview of the Topics for Midterm I
Review of the Topics for Midterm I STA 100 Lecture 9 I. Introduction The objective of statistics is to make inferences about a population based on information contained in a sample. A population is the
More informationThe Normal Probability Distribution
1 The Normal Probability Distribution Key Definitions Probability Density Function: An equation used to compute probabilities for continuous random variables where the output value is greater than zero
More informationExamples: Random Variables. Discrete and Continuous Random Variables. Probability Distributions
Random Variables Examples: Random variable a variable (typically represented by x) that takes a numerical value by chance. Number of boys in a randomly selected family with three children. Possible values:
More informationCentral Limit Theorem (cont d) 7/28/2006
Central Limit Theorem (cont d) 7/28/2006 Central Limit Theorem for Binomial Distributions Theorem. For the binomial distribution b(n, p, j) we have lim npq b(n, p, np + x npq ) = φ(x), n where φ(x) is
More informationOverview. Definitions. Definitions. Graphs. Chapter 5 Probability Distributions. probability distributions
Chapter 5 Probability Distributions 5-1 Overview 5-2 Random Variables 5-3 Binomial Probability Distributions 5-4 Mean, Variance, and Standard Deviation for the Binomial Distribution 5-5 The Poisson Distribution
More informationDiscrete Probability Distribution
1 Discrete Probability Distribution Key Definitions Discrete Random Variable: Has a countable number of values. This means that each data point is distinct and separate. Continuous Random Variable: Has
More informationChapter 7. Sampling Distributions and the Central Limit Theorem
Chapter 7. Sampling Distributions and the Central Limit Theorem 1 Introduction 2 Sampling Distributions related to the normal distribution 3 The central limit theorem 4 The normal approximation to binomial
More informationMATH 10 INTRODUCTORY STATISTICS
MATH 10 INTRODUCTORY STATISTICS Ramesh Yapalparvi Week 3 Chapter 5 Probability Chapter 7 Normal Distribution Chapter 8 Advanced Graphs Chapter 9 Sampling Distributions ß today s lecture Sampling distributions
More informationThe Binomial Probability Distribution
The Binomial Probability Distribution MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2017 Objectives After this lesson we will be able to: determine whether a probability
More informationSampling & populations
Sampling & populations Sample proportions Sampling distribution - small populations Sampling distribution - large populations Sampling distribution - normal distribution approximation Mean & variance of
More informationMath Week in Review #10. Experiments with two outcomes ( success and failure ) are called Bernoulli or binomial trials.
Math 141 Spring 2006 c Heather Ramsey Page 1 Section 8.4 - Binomial Distribution Math 141 - Week in Review #10 Experiments with two outcomes ( success and failure ) are called Bernoulli or binomial trials.
More informationProbability is the tool used for anticipating what the distribution of data should look like under a given model.
AP Statistics NAME: Exam Review: Strand 3: Anticipating Patterns Date: Block: III. Anticipating Patterns: Exploring random phenomena using probability and simulation (20%-30%) Probability is the tool used
More informationSTAT243 LS: Intro to Probability and Statistics Final Exam, Mar 20, 2017 KEY
STAT243 LS: Intro to Probability and Statistics Final Exam, Mar 20, 2017 KEY This is a 110-min exam. Students may use a page of note (front and back), and a calculator, but nothing else is allowed. 1.
More informationLet X be the number that comes up on the next roll of the die.
Chapter 6 - Discrete Probability Distributions 6.1 Random Variables Introduction If we roll a fair die, the possible outcomes are the numbers 1, 2, 3, 4, 5, and 6, and each of these numbers has probability
More informationCHAPTER 6 Random Variables
CHAPTER 6 Random Variables 6.1 Discrete and Continuous Random Variables The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers Discrete and Continuous Random
More informationClass 16. Daniel B. Rowe, Ph.D. Department of Mathematics, Statistics, and Computer Science. Marquette University MATH 1700
Class 16 Daniel B. Rowe, Ph.D. Department of Mathematics, Statistics, and Computer Science Copyright 013 by D.B. Rowe 1 Agenda: Recap Chapter 7. - 7.3 Lecture Chapter 8.1-8. Review Chapter 6. Problem Solving
More informationStatistics for Managers Using Microsoft Excel 7 th Edition
Statistics for Managers Using Microsoft Excel 7 th Edition Chapter 7 Sampling Distributions Statistics for Managers Using Microsoft Excel 7e Copyright 2014 Pearson Education, Inc. Chap 7-1 Learning Objectives
More informationSTAT Chapter 7: Confidence Intervals
STAT 515 -- Chapter 7: Confidence Intervals With a point estimate, we used a single number to estimate a parameter. We can also use a set of numbers to serve as reasonable estimates for the parameter.
More informationConfidence Intervals for Large Sample Proportions
Confidence Intervals for Large Sample Proportions Dr Tom Ilvento Department of Food and Resource Economics Overview Confidence Intervals C.I. We will start with large sample C.I. for proportions, using
More informationAP Statistics Ch 8 The Binomial and Geometric Distributions
Ch 8.1 The Binomial Distributions The Binomial Setting A situation where these four conditions are satisfied is called a binomial setting. 1. Each observation falls into one of just two categories, which
More informationguessing Bluman, Chapter 5 2
Bluman, Chapter 5 1 guessing Suppose there is multiple choice quiz on a subject you don t know anything about. 15 th Century Russian Literature; Nuclear physics etc. You have to guess on every question.
More informationMidTerm 1) Find the following (round off to one decimal place):
MidTerm 1) 68 49 21 55 57 61 70 42 59 50 66 99 Find the following (round off to one decimal place): Mean = 58:083, round off to 58.1 Median = 58 Range = max min = 99 21 = 78 St. Deviation = s = 8:535,
More informationSampling and sampling distribution
Sampling and sampling distribution September 12, 2017 STAT 101 Class 5 Slide 1 Outline of Topics 1 Sampling 2 Sampling distribution of a mean 3 Sampling distribution of a proportion STAT 101 Class 5 Slide
More informationHomework: Due Wed, Nov 3 rd Chapter 8, # 48a, 55c and 56 (count as 1), 67a
Homework: Due Wed, Nov 3 rd Chapter 8, # 48a, 55c and 56 (count as 1), 67a Announcements: There are some office hour changes for Nov 5, 8, 9 on website Week 5 quiz begins after class today and ends at
More informationIn a binomial experiment of n trials, where p = probability of success and q = probability of failure. mean variance standard deviation
Name In a binomial experiment of n trials, where p = probability of success and q = probability of failure mean variance standard deviation µ = n p σ = n p q σ = n p q Notation X ~ B(n, p) The probability
More informationConfidence Intervals and Sample Size
Confidence Intervals and Sample Size Chapter 6 shows us how we can use the Central Limit Theorem (CLT) to 1. estimate a population parameter (such as the mean or proportion) using a sample, and. determine
More informationData Analysis and Statistical Methods Statistics 651
Review of previous lecture: Why confidence intervals? Data Analysis and Statistical Methods Statistics 651 http://www.stat.tamu.edu/~suhasini/teaching.html Suhasini Subba Rao Suppose you want to know the
More informationThe Normal Approximation to the Binomial Distribution
7 6 The Normal Approximation to the Binomial Distribution Objective 7. Use the normal approximation to compute probabilities for a binomial variable. The normal distribution is often used to solve problems
More informationChapter 3 Discrete Random Variables and Probability Distributions
Chapter 3 Discrete Random Variables and Probability Distributions Part 3: Special Discrete Random Variable Distributions Section 3.5 Discrete Uniform Section 3.6 Bernoulli and Binomial Others sections
More informationAMS 7 Sampling Distributions, Central limit theorem, Confidence Intervals Lecture 4
AMS 7 Sampling Distributions, Central limit theorem, Confidence Intervals Lecture 4 Department of Applied Mathematics and Statistics, University of California, Santa Cruz Summer 2014 1 / 26 Sampling Distributions!!!!!!
More informationChapter 7. Sampling Distributions and the Central Limit Theorem
Chapter 7. Sampling Distributions and the Central Limit Theorem 1 Introduction 2 Sampling Distributions related to the normal distribution 3 The central limit theorem 4 The normal approximation to binomial
More informationMATH 3200 Exam 3 Dr. Syring
. Suppose n eligible voters are polled (randomly sampled) from a population of size N. The poll asks voters whether they support or do not support increasing local taxes to fund public parks. Let M be
More informationSampling Distributions For Counts and Proportions
Sampling Distributions For Counts and Proportions IPS Chapter 5.1 2009 W. H. Freeman and Company Objectives (IPS Chapter 5.1) Sampling distributions for counts and proportions Binomial distributions for
More informationMA 1125 Lecture 12 - Mean and Standard Deviation for the Binomial Distribution. Objectives: Mean and standard deviation for the binomial distribution.
MA 5 Lecture - Mean and Standard Deviation for the Binomial Distribution Friday, September 9, 07 Objectives: Mean and standard deviation for the binomial distribution.. Mean and Standard Deviation of the
More informationECON 214 Elements of Statistics for Economists 2016/2017
ECON 214 Elements of Statistics for Economists 2016/2017 Topic The Normal Distribution Lecturer: Dr. Bernardin Senadza, Dept. of Economics bsenadza@ug.edu.gh College of Education School of Continuing and
More informationStatistical Methods in Practice STAT/MATH 3379
Statistical Methods in Practice STAT/MATH 3379 Dr. A. B. W. Manage Associate Professor of Mathematics & Statistics Department of Mathematics & Statistics Sam Houston State University Overview 6.1 Discrete
More informationValue (x) probability Example A-2: Construct a histogram for population Ψ.
Calculus 111, section 08.x The Central Limit Theorem notes by Tim Pilachowski If you haven t done it yet, go to the Math 111 page and download the handout: Central Limit Theorem supplement. Today s lecture
More informationSec$on 6.1: Discrete and Con.nuous Random Variables. Tuesday, November 14 th, 2017
Sec$on 6.1: Discrete and Con.nuous Random Variables Tuesday, November 14 th, 2017 Discrete and Continuous Random Variables Learning Objectives After this section, you should be able to: ü COMPUTE probabilities
More informationCHAPTER 5 SAMPLING DISTRIBUTIONS
CHAPTER 5 SAMPLING DISTRIBUTIONS Sampling Variability. We will visualize our data as a random sample from the population with unknown parameter μ. Our sample mean Ȳ is intended to estimate population mean
More informationName PID Section # (enrolled)
STT 315 - Lecture 3 Instructor: Aylin ALIN 04/02/2014 Midterm # 2 A Name PID Section # (enrolled) * The exam is closed book and 80 minutes. * You may use a calculator and the formula sheet that you brought
More informationDetermine whether the given procedure results in a binomial distribution. If not, state the reason why.
Math 5.3 Binomial Probability Distributions Name 1) Binomial Distrbution: Determine whether the given procedure results in a binomial distribution. If not, state the reason why. 2) Rolling a single die
More informationTheoretical Foundations
Theoretical Foundations Probabilities Monia Ranalli monia.ranalli@uniroma2.it Ranalli M. Theoretical Foundations - Probabilities 1 / 27 Objectives understand the probability basics quantify random phenomena
More informationMATH 264 Problem Homework I
MATH Problem Homework I Due to December 9, 00@:0 PROBLEMS & SOLUTIONS. A student answers a multiple-choice examination question that offers four possible answers. Suppose that the probability that the
More informationCHAPTER 5 Sampling Distributions
CHAPTER 5 Sampling Distributions 5.1 The possible values of p^ are 0, 1/3, 2/3, and 1. These correspond to getting 0 persons with lung cancer, 1 with lung cancer, 2 with lung cancer, and all 3 with lung
More informationMath Tech IIII, Mar 6
Math Tech IIII, Mar 6 The Binomial Distribution II Book Sections: 4.2 Essential Questions: How can I compute the probability of any event? What do I need to know about the binomial distribution? Standards:
More information3. The n observations are independent. Knowing the result of one observation tells you nothing about the other observations.
Binomial and Geometric Distributions - Terms and Formulas Binomial Experiments - experiments having all four conditions: 1. Each observation falls into one of two categories we call them success or failure.
More information5.1 Personal Probability
5. Probability Value Page 1 5.1 Personal Probability Although we think probability is something that is confined to math class, in the form of personal probability it is something we use to make decisions
More informationUnit 04 Review. Probability Rules
Unit 04 Review Probability Rules A sample space contains all the possible outcomes observed in a trial of an experiment, a survey, or some random phenomenon. The sum of the probabilities for all possible
More informationReview: Population, sample, and sampling distributions
Review: Population, sample, and sampling distributions A population with mean µ and standard deviation σ For instance, µ = 0, σ = 1 0 1 Sample 1, N=30 Sample 2, N=30 Sample 100000000000 InterquartileRange
More information4.3 Normal distribution
43 Normal distribution Prof Tesler Math 186 Winter 216 Prof Tesler 43 Normal distribution Math 186 / Winter 216 1 / 4 Normal distribution aka Bell curve and Gaussian distribution The normal distribution
More informationChapter Six Probability Distributions
6.1 Probability Distributions Discrete Random Variable Chapter Six Probability Distributions x P(x) 2 0.08 4 0.13 6 0.25 8 0.31 10 0.16 12 0.01 Practice. Construct a probability distribution for the number
More informationCH 5 Normal Probability Distributions Properties of the Normal Distribution
Properties of the Normal Distribution Example A friend that is always late. Let X represent the amount of minutes that pass from the moment you are suppose to meet your friend until the moment your friend
More informationStatistical Intervals (One sample) (Chs )
7 Statistical Intervals (One sample) (Chs 8.1-8.3) Confidence Intervals The CLT tells us that as the sample size n increases, the sample mean X is close to normally distributed with expected value µ and
More informationEstimation. Focus Points 10/11/2011. Estimating p in the Binomial Distribution. Section 7.3
Estimation 7 Copyright Cengage Learning. All rights reserved. Section 7.3 Estimating p in the Binomial Distribution Copyright Cengage Learning. All rights reserved. Focus Points Compute the maximal length
More informationHomework: Due Wed, Feb 20 th. Chapter 8, # 60a + 62a (count together as 1), 74, 82
Announcements: Week 5 quiz begins at 4pm today and ends at 3pm on Wed If you take more than 20 minutes to complete your quiz, you will only receive partial credit. (It doesn t cut you off.) Today: Sections
More informationChapter. Section 4.2. Chapter 4. Larson/Farber 5 th ed 1. Chapter Outline. Discrete Probability Distributions. Section 4.
Chapter Discrete Probability s Chapter Outline 1 Probability s 2 Binomial s 3 More Discrete Probability s Copyright 2015, 2012, and 2009 Pearson Education, Inc 1 Copyright 2015, 2012, and 2009 Pearson
More informationChapter 7. Sampling Distributions
Chapter 7 Sampling Distributions Section 7.1 Sampling Distributions and the Central Limit Theorem Sampling Distributions Sampling distribution The probability distribution of a sample statistic. Formed
More information3. The n observations are independent. Knowing the result of one observation tells you nothing about the other observations.
Binomial and Geometric Distributions - Terms and Formulas Binomial Experiments - experiments having all four conditions: 1. Each observation falls into one of two categories we call them success or failure.
More information8.1 Binomial Distributions
8.1 Binomial Distributions The Binomial Setting The 4 Conditions of a Binomial Setting: 1.Each observation falls into 1 of 2 categories ( success or fail ) 2 2.There is a fixed # n of observations. 3.All
More informationKey Concept. 155S6.6_3 Normal as Approximation to Binomial. March 02, 2011
MAT 155 Statistical Analysis Dr. Claude Moore Cape Fear Community College Chapter 6 Normal Probability Distributions 6 1 Review and Preview 6 2 The Standard Normal Distribution 6 3 Applications of Normal
More informationRandom Variables. Chapter 6: Random Variables 2/2/2014. Discrete and Continuous Random Variables. Transforming and Combining Random Variables
Chapter 6: Random Variables Section 6.3 The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE Random Variables 6.1 6.2 6.3 Discrete and Continuous Random Variables Transforming and Combining
More informationStatistics Class 15 3/21/2012
Statistics Class 15 3/21/2012 Quiz 1. Cans of regular Pepsi are labeled to indicate that they contain 12 oz. Data Set 17 in Appendix B lists measured amounts for a sample of Pepsi cans. The same statistics
More information1 Inferential Statistic
1 Inferential Statistic Population versus Sample, parameter versus statistic A population is the set of all individuals the researcher intends to learn about. A sample is a subset of the population and
More informationChapter 7 Study Guide: The Central Limit Theorem
Chapter 7 Study Guide: The Central Limit Theorem Introduction Why are we so concerned with means? Two reasons are that they give us a middle ground for comparison and they are easy to calculate. In this
More information4.2 Bernoulli Trials and Binomial Distributions
Arkansas Tech University MATH 3513: Applied Statistics I Dr. Marcel B. Finan 4.2 Bernoulli Trials and Binomial Distributions A Bernoulli trial 1 is an experiment with exactly two outcomes: Success and
More informationNormal distribution Approximating binomial distribution by normal 2.10 Central Limit Theorem
1.1.2 Normal distribution 1.1.3 Approimating binomial distribution by normal 2.1 Central Limit Theorem Prof. Tesler Math 283 Fall 216 Prof. Tesler 1.1.2-3, 2.1 Normal distribution Math 283 / Fall 216 1
More informationChapter 5. Discrete Probability Distributions. McGraw-Hill, Bluman, 7 th ed, Chapter 5 1
Chapter 5 Discrete Probability Distributions McGraw-Hill, Bluman, 7 th ed, Chapter 5 1 Chapter 5 Overview Introduction 5-1 Probability Distributions 5-2 Mean, Variance, Standard Deviation, and Expectation
More informationSampling Distributions Chapter 18
Sampling Distributions Chapter 18 Parameter vs Statistic Example: Identify the population, the parameter, the sample, and the statistic in the given settings. a) The Gallup Poll asked a random sample of
More informationMath Tech IIII, Mar 13
Math Tech IIII, Mar 13 The Binomial Distribution III Book Sections: 4.2 Essential Questions: What do I need to know about the binomial distribution? Standards: DA-5.6 What Makes a Binomial Experiment?
More informationChapter 3. Discrete Probability Distributions
Chapter 3 Discrete Probability Distributions 1 Chapter 3 Overview Introduction 3-1 The Binomial Distribution 3-2 Other Types of Distributions 2 Chapter 3 Objectives Find the exact probability for X successes
More informationBinomial Random Variables. Binomial Random Variables
Bernoulli Trials Definition A Bernoulli trial is a random experiment in which there are only two possible outcomes - success and failure. 1 Tossing a coin and considering heads as success and tails as
More information+ Chapter 7. Random Variables. Chapter 7: Random Variables 2/26/2015. Transforming and Combining Random Variables
+ Chapter 7: Random Variables Section 7.1 Discrete and Continuous Random Variables The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE + Chapter 7 Random Variables 7.1 7.2 7.2 Discrete
More informationLecture Slides. Elementary Statistics Tenth Edition. by Mario F. Triola. and the Triola Statistics Series
Lecture Slides Elementary Statistics Tenth Edition and the Triola Statistics Series by Mario F. Triola Slide 1 Chapter 5 Probability Distributions 5-1 Overview 5-2 Random Variables 5-3 Binomial Probability
More informationChapter 5 Probability Distributions. Section 5-2 Random Variables. Random Variable Probability Distribution. Discrete and Continuous Random Variables
Chapter 5 Probability Distributions Section 5-2 Random Variables 5-2 Random Variables 5-3 Binomial Probability Distributions 5-4 Mean, Variance and Standard Deviation for the Binomial Distribution Random
More informationProbability & Sampling The Practice of Statistics 4e Mostly Chpts 5 7
Probability & Sampling The Practice of Statistics 4e Mostly Chpts 5 7 Lew Davidson (Dr.D.) Mallard Creek High School Lewis.Davidson@cms.k12.nc.us 704-786-0470 Probability & Sampling The Practice of Statistics
More informationHOMEWORK: Due Mon 11/8, Chapter 9: #15, 25, 37, 44
This week: Chapter 9 (will do 9.6 to 9.8 later, with Chap. 11) Understanding Sampling Distributions: Statistics as Random Variables ANNOUNCEMENTS: Shandong Min will give the lecture on Friday. See website
More information