Y i % (% ( ( ' & ( # % s 2 = ( ( Review - order of operations. Samples and populations. Review - order of operations. Review - order of operations
|
|
|
- Austen Manning
- 5 years ago
- Views:
Transcription
1 Review - order of operations Samples and populations Estimating with uncertainty s 2 = # % # n & % % $ n "1'% % $ n ) i=1 Y i 2 n & "Y 2 ' Review - order of operations Review - order of operations 1. Parentheses 2. Exponents and roots 3. Multiply and divide 4. Add and subtract s 2 = # % # n & % % $ n "1'% % $ n ) i=1 Y i 2 n & "Y 2 '
2 Review - order of operations Review - types of variables s 2 = # % # n & % % $ n "1'% % $ n ) i=1 Y i 2 n & "Y 2 ' Categorical variables For example, country of birth Numerical variables For example, student height Review - types of variables Review - types of variables Categorical variables Categorical variables Nominal Ordinal Numerical variables Discrete Numerical variables Discrete Continuous Continuous
3 Review - types of variables Categorical variables Nominal - no natural order Ordinal - can be placed in an order Review - types of variables Categorical variables Nominal - no natural order Example - country of birth Ordinal - can be placed in an order Review - types of variables Categorical variables Nominal - no natural order Example - country of birth Ordinal - can be placed in an order Example - educational experience Some high school, high school diploma, some college, college degree, masters degree, PhD Sampling from a population We often sample from a population Consider random samples Each individual has an equal and identical probability of being selected
4 Body mass of 400 humans Random sample of 10 people
5 Population mean: µ = 70.8 kg Another sample Population mean: µ = 70.8 kg Sample mean: x = 76.7 kg
6 Population mean: µ = 70.8 kg Sample mean: x = 69.2 kg n = 20,290 What if we do this many times? Example: gene length
7 n = 20,290 µ = ! = Sample histogram n = 100 Y = s = Y = s = Y = s = Y = s = Y = s =
8 Sampling distribution of the mean Sampling distribution of the mean Y = s = Y = s = samples Y = s = Y = s = Sampling distribution of the mean Sampling distribution of the mean
9 µ = Y = s = Y = s = Sampling distribution of the mean Mean of means: Y = s = Y = s = Sampling distribution of the standard deviation Sampling distribution of the standard deviation s = s = s = s =
10 Sampling distribution of the standard deviation Sampling distribution of the standard deviation 100 samples Population! = Mean sample s = samples Population! = Mean sample s = Sampling distribution of the mean, n=10 Sampling distribution of the mean, n=10 Sampling distribution of the mean, n=100 Sampling distribution of the mean, n=100 Sampling distribution of the mean, n = 1000 Sampling distribution of the mean, n = 1000
11 Larger sample size Precise Imprecise Precise Imprecise Unbiased Unbiased Biased Biased Group activity #2 Form groups of size 2-5 Get out a blank sheet of paper Write everyone s full name on the paper
12 How many toes do aliens have? Instructions You have measurements from a population of 400 aliens Use your random number table to select a sample of ten measurements Calculate your sample mean and, if you have a calculator or a large brain, your sample standard deviation On your paper, answer the following: 1. What was your sample mean and standard deviation? 2. How did you randomly choose your sample?
13 Distribution of the sample mean No matter what the frequency distribution of the population: The sample mean has an approximately bell-shaped normal) distribution Especially for large n large samples) How precise is any one estimated sample mean? The standard error of an estimate is the standard deviation of its sampling distribution. The standard error predicts the sampling error of the estimate. Standard error of the mean " µ = " n
14 Estimate of the standard error of the mean SE Y = s n Confidence interval Confidence interval a range of values surrounding the sample estimate that is likely to contain the population parameter 95% confidence interval plausible range for a parameter based on the data The 2SE rule-of-thumb Confidence interval The interval from Y! 2 SE to Y + 2 SE provides a rough estimate of the 95% confidence interval for the mean. Y Y
15 Pseudoreplication The error that occurs when samples are not independent, but they are treated as though they are. Example: The transylvania effect A study of 130,000 calls for police assistance in 1980 found that they were more likely than chance to occur during a full moon. Example: The transylvania effect A study of 130,000 calls for police assistance in 1980 found that they were more likely than chance to occur during a full moon. Problem: There may have been 130,000 calls in the data set, but there were only 13 full moons in These data are not independent.
Making Sense of Cents
Name: Date: Making Sense of Cents Exploring the Central Limit Theorem Many of the variables that you have studied so far in this class have had a normal distribution. You have used a table of the normal
Chapter 8 Estimation
Chapter 8 Estimation There are two important forms of statistical inference: estimation (Confidence Intervals) Hypothesis Testing Statistical Inference drawing conclusions about populations based on samples
ECON 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
ECON 214 Elements of Statistics for Economists
ECON 214 Elements of Statistics for Economists Session 7 The Normal Distribution Part 1 Lecturer: Dr. Bernardin Senadza, Dept. of Economics Contact Information: bsenadza@ug.edu.gh College of Education
AP Statistics Chapter 6 - Random Variables
AP Statistics Chapter 6 - Random 6.1 Discrete and Continuous Random Objective: Recognize and define discrete random variables, and construct a probability distribution table and a probability histogram
Chapter 7 Sampling Distributions and Point Estimation of Parameters
Chapter 7 Sampling Distributions and Point Estimation of Parameters Part 1: Sampling Distributions, the Central Limit Theorem, Point Estimation & Estimators Sections 7-1 to 7-2 1 / 25 Statistical Inferences
22.2 Shape, Center, and Spread
Name Class Date 22.2 Shape, Center, and Spread Essential Question: Which measures of center and spread are appropriate for a normal distribution, and which are appropriate for a skewed distribution? Eplore
Normal Probability Distributions
Normal Probability Distributions Properties of Normal Distributions The most important probability distribution in statistics is the normal distribution. Normal curve A normal distribution is a continuous
Chapter 7: SAMPLING DISTRIBUTIONS & POINT ESTIMATION OF PARAMETERS
Chapter 7: SAMPLING DISTRIBUTIONS & POINT ESTIMATION OF PARAMETERS Part 1: Introduction Sampling Distributions & the Central Limit Theorem Point Estimation & Estimators Sections 7-1 to 7-2 Sample data
A continuous random variable is one that can theoretically take on any value on some line interval. We use f ( x)
Section 6-2 I. Continuous Probability Distributions A continuous random variable is one that can theoretically take on any value on some line interval. We use f ( x) to represent a probability density
Determining Sample Size. Slide 1 ˆ ˆ. p q n E = z α / 2. (solve for n by algebra) n = E 2
Determining Sample Size Slide 1 E = z α / 2 ˆ ˆ p q n (solve for n by algebra) n = ( zα α / 2) 2 p ˆ qˆ E 2 Sample Size for Estimating Proportion p When an estimate of ˆp is known: Slide 2 n = ˆ ˆ ( )
Math 140 Introductory Statistics. Next midterm May 1
Math 140 Introductory Statistics Next midterm May 1 8.1 Confidence intervals 54% of Americans approve the job the president is doing with a margin error of 3% 55% of 18-29 year olds consider themselves
Chapter 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
Key Objectives. Module 2: The Logic of Statistical Inference. Z-scores. SGSB Workshop: Using Statistical Data to Make Decisions
SGSB Workshop: Using Statistical Data to Make Decisions Module 2: The Logic of Statistical Inference Dr. Tom Ilvento January 2006 Dr. Mugdim Pašić Key Objectives Understand the logic of statistical inference
8.1 Estimation of the Mean and Proportion
8.1 Estimation of the Mean and Proportion Statistical inference enables us to make judgments about a population on the basis of sample information. The mean, standard deviation, and proportions of a population
MA131 Lecture 8.2. The normal distribution curve can be considered as a probability distribution curve for normally distributed variables.
Normal distribution curve as probability distribution curve The normal distribution curve can be considered as a probability distribution curve for normally distributed variables. The area under the normal
The Central Limit Theorem (Solutions) COR1-GB.1305 Statistics and Data Analysis
The Central Limit Theorem (Solutions) COR1-GB1305 Statistics and Data Analysis 1 You draw a random sample of size n = 64 from a population with mean µ = 50 and standard deviation σ = 16 From this, you
CHAPTER 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
5.1 Mean, Median, & Mode
5.1 Mean, Median, & Mode definitions Mean: Median: Mode: Example 1 The Blue Jays score these amounts of runs in their last 9 games: 4, 7, 2, 4, 10, 5, 6, 7, 7 Find the mean, median, and mode: Example 2
ECO220Y 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
Statistics 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
Chapter 15: Sampling distributions
=true true Chapter 15: Sampling distributions Objective (1) Get "big picture" view on drawing inferences from statistical studies. (2) Understand the concept of sampling distributions & sampling variability.
CHAPTER 6 Random Variables
CHAPTER 6 Random Variables 6.2 Transforming and Combining Random Variables The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers 6.2 Reading Quiz (T or F)
1 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
BIOL The Normal Distribution and the Central Limit Theorem
BIOL 300 - The Normal Distribution and the Central Limit Theorem In the first week of the course, we introduced a few measures of center and spread, and discussed how the mean and standard deviation are
( ) P = = =
1. On a lunch counter, there are 5 oranges and 6 apples. If 3 pieces of fruit are selected, find the probability that 1 orange and apples are selected. Order does not matter Combinations: 5C1 (1 ) 6C P
Chapter 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
STAT Chapter 6 The Standard Deviation (SD) as a Ruler and The Normal Model
STAT 203 - Chapter 6 The Standard Deviation (SD) as a Ruler and The Normal Model In Chapter 5, we introduced a few measures of center and spread, and discussed how the mean and standard deviation are good
Chapter 4 Variability
Chapter 4 Variability PowerPoint Lecture Slides Essentials of Statistics for the Behavioral Sciences Seventh Edition by Frederick J Gravetter and Larry B. Wallnau Chapter 4 Learning Outcomes 1 2 3 4 5
The topics in this section are related and necessary topics for both course objectives.
2.5 Probability Distributions The topics in this section are related and necessary topics for both course objectives. A probability distribution indicates how the probabilities are distributed for outcomes
Introduction to Statistics I
Introduction to Statistics I Keio University, Faculty of Economics Continuous random variables Simon Clinet (Keio University) Intro to Stats November 1, 2018 1 / 18 Definition (Continuous random variable)
3.3-Measures of Variation
3.3-Measures of Variation Variation: Variation is a measure of the spread or dispersion of a set of data from its center. Common methods of measuring variation include: 1. Range. Standard Deviation 3.
ECO220Y Continuous Probability Distributions: Normal Readings: Chapter 9, section 9.10
ECO220Y Continuous Probability Distributions: Normal Readings: Chapter 9, section 9.10 Fall 2011 Lecture 8 Part 2 (Fall 2011) Probability Distributions Lecture 8 Part 2 1 / 23 Normal Density Function f
Math 227 Elementary Statistics. Bluman 5 th edition
Math 227 Elementary Statistics Bluman 5 th edition CHAPTER 6 The Normal Distribution 2 Objectives Identify distributions as symmetrical or skewed. Identify the properties of the normal distribution. Find
Diploma in Business Administration Part 2. Quantitative Methods. Examiner s Suggested Answers
Cumulative frequency Diploma in Business Administration Part Quantitative Methods Examiner s Suggested Answers Question 1 Cumulative Frequency Curve 1 9 8 7 6 5 4 3 1 5 1 15 5 3 35 4 45 Weeks 1 (b) x f
11.5: Normal Distributions
11.5: Normal Distributions 11.5.1 Up to now, we ve dealt with discrete random variables, variables that take on only a finite (or countably infinite we didn t do these) number of values. A continuous random
Shifting our focus. We were studying statistics (data, displays, sampling...) The next few lectures focus on probability (randomness) Why?
Probability Introduction Shifting our focus We were studying statistics (data, displays, sampling...) The next few lectures focus on probability (randomness) Why? What is Probability? Probability is used
Sampling Distributions and the Central Limit Theorem
Sampling Distributions and the Central Limit Theorem February 18 Data distributions and sampling distributions So far, we have discussed the distribution of data (i.e. of random variables in our sample,
Overview. 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
4.2 Probability Distributions
4.2 Probability Distributions Definition. A random variable is a variable whose value is a numerical outcome of a random phenomenon. The probability distribution of a random variable tells us what the
Both the quizzes and exams are closed book. However, For quizzes: Formulas will be provided with quiz papers if there is any need.
Both the quizzes and exams are closed book. However, For quizzes: Formulas will be provided with quiz papers if there is any need. For exams (MD1, MD2, and Final): You may bring one 8.5 by 11 sheet of
Chapter 6: Random Variables
Chapter 6: Random Variables Section 6.1 Discrete and Continuous Random Variables The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE Chapter 6 Random Variables 6.1 Discrete and Continuous
Chapter 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
Value (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
Discrete 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
Linear Regression with One Regressor
Linear Regression with One Regressor Michael Ash Lecture 9 Linear Regression with One Regressor Review of Last Time 1. The Linear Regression Model The relationship between independent X and dependent Y
Lecture 6: Chapter 6
Lecture 6: Chapter 6 C C Moxley UAB Mathematics 3 October 16 6.1 Continuous Probability Distributions Last week, we discussed the binomial probability distribution, which was discrete. 6.1 Continuous Probability
Estimation Y 3. Confidence intervals I, Feb 11,
Estimation Example: Cholesterol levels of heart-attack patients Data: Observational study at a Pennsylvania medical center blood cholesterol levels patients treated for heart attacks measurements 2, 4,
IOP 201-Q (Industrial Psychological Research) Tutorial 5
IOP 201-Q (Industrial Psychological Research) Tutorial 5 TRUE/FALSE [1 point each] Indicate whether the sentence or statement is true or false. 1. To establish a cause-and-effect relation between two variables,
Sampling 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
Probability & 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
Data Analysis and Statistical Methods Statistics 651
Data Analysis and Statistical Methods Statistics 651 http://wwwstattamuedu/~suhasini/teachinghtml Suhasini Subba Rao Review of previous lecture The main idea in the previous lecture is that the sample
Chapter 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
Example - Let X be the number of boys in a 4 child family. Find the probability distribution table:
Chapter8 Probability Distributions and Statistics Section 8.1 Distributions of Random Variables tthe value of the result of the probability experiment is a RANDOM VARIABLE. Example - Let X be the number
Statistical 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
Lecture 9. Probability Distributions. Outline. Outline
Outline Lecture 9 Probability Distributions 6-1 Introduction 6- Probability Distributions 6-3 Mean, Variance, and Expectation 6-4 The Binomial Distribution Outline 7- Properties of the Normal Distribution
CHAPTER 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
MA131 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
Statistics and Probability
Statistics and Probability Continuous RVs (Normal); Confidence Intervals Outline Continuous random variables Normal distribution CLT Point estimation Confidence intervals http://www.isrec.isb-sib.ch/~darlene/geneve/
Chapter 23: accuracy of averages
Chapter 23: accuracy of averages Context: previous chapters...................................................... 2 Context: previous chapters...................................................... 3 Context:
CHAPTER 7 INTRODUCTION TO SAMPLING DISTRIBUTIONS
CHAPTER 7 INTRODUCTION TO SAMPLING DISTRIBUTIONS Note: This section uses session window commands instead of menu choices CENTRAL LIMIT THEOREM (SECTION 7.2 OF UNDERSTANDABLE STATISTICS) The Central Limit
Lecture 9. Probability Distributions
Lecture 9 Probability Distributions Outline 6-1 Introduction 6-2 Probability Distributions 6-3 Mean, Variance, and Expectation 6-4 The Binomial Distribution Outline 7-2 Properties of the Normal Distribution
8.2 The Standard Deviation as a Ruler Chapter 8 The Normal and Other Continuous Distributions 8-1
8.2 The Standard Deviation as a Ruler Chapter 8 The Normal and Other Continuous Distributions For Example: On August 8, 2011, the Dow dropped 634.8 points, sending shock waves through the financial community.
Chapter 4: Estimation
Slide 4.1 Chapter 4: Estimation Estimation is the process of using sample data to draw inferences about the population Sample information x, s Inferences Population parameters µ,σ Slide 4. Point and interval
Chapter Seven: Confidence Intervals and Sample Size
Chapter Seven: Confidence Intervals and Sample Size A point estimate is: The best point estimate of the population mean µ is the sample mean X. Three Properties of a Good Estimator 1. Unbiased 2. Consistent
STAT Chapter 6 The Standard Deviation (SD) as a Ruler and The Normal Model
STAT 203 - Chapter 6 The Standard Deviation (SD) as a Ruler and The Normal Model In Chapter 5, we introduced a few measures of center and spread, and discussed how the mean and standard deviation are good
Random Variables. 6.1 Discrete and Continuous Random Variables. Probability Distribution. Discrete Random Variables. Chapter 6, Section 1
6.1 Discrete and Continuous Random Variables Random Variables A random variable, usually written as X, is a variable whose possible values are numerical outcomes of a random phenomenon. There are two types
NORMAL RANDOM VARIABLES (Normal or gaussian distribution)
NORMAL RANDOM VARIABLES (Normal or gaussian distribution) Many variables, as pregnancy lengths, foot sizes etc.. exhibit a normal distribution. The shape of the distribution is a symmetric bell shape.
A probability distribution shows the possible outcomes of an experiment and the probability of each of these outcomes.
Introduction In the previous chapter we discussed the basic concepts of probability and described how the rules of addition and multiplication were used to compute probabilities. In this chapter we expand
Lecture Slides. Elementary Statistics Tenth Edition. by Mario F. Triola. and the Triola Statistics Series. Slide 1
Lecture Slides Elementary Statistics Tenth Edition and the Triola Statistics Series by Mario F. Triola Slide 1 Chapter 6 Normal Probability Distributions 6-1 Overview 6-2 The Standard Normal Distribution
The 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
Statistics 13 Elementary Statistics
Statistics 13 Elementary Statistics Summer Session I 2012 Lecture Notes 5: Estimation with Confidence intervals 1 Our goal is to estimate the value of an unknown population parameter, such as a population
Sec$on 6.1: Discrete and Con.nuous Random Variables. Tuesday, November 14 th, 2017
Sec$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
Uniform Probability Distribution. Continuous Random Variables &
Continuous Random Variables & What is a Random Variable? It is a quantity whose values are real numbers and are determined by the number of desired outcomes of an experiment. Is there any special Random
Math 2311 Bekki George Office Hours: MW 11am to 12:45pm in 639 PGH Online Thursdays 4-5:30pm And by appointment
Math 2311 Bekki George bekki@math.uh.edu Office Hours: MW 11am to 12:45pm in 639 PGH Online Thursdays 4-5:30pm And by appointment Class webpage: http://www.math.uh.edu/~bekki/math2311.html Math 2311 Class
Example - Let X be the number of boys in a 4 child family. Find the probability distribution table:
Chapter7 Probability Distributions and Statistics Distributions of Random Variables tthe value of the result of the probability experiment is a RANDOM VARIABLE. Example - Let X be the number of boys in
STATISTICS - CLUTCH CH.9: SAMPLING DISTRIBUTIONS: MEAN.
!! www.clutchprep.com SAMPLING DISTRIBUTIONS (MEANS) As of now, the normal distributions we have worked with only deal with the population of observations Example: What is the probability of randomly selecting
Overview. 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
The Normal Distribution
5.1 Introduction to Normal Distributions and the Standard Normal Distribution Section Learning objectives: 1. How to interpret graphs of normal probability distributions 2. How to find areas under the
Chapter 7. Random Variables
Chapter 7 Random Variables Making quantifiable meaning out of categorical data Toss three coins. What does the sample space consist of? HHH, HHT, HTH, HTT, TTT, TTH, THT, THH In statistics, we are most
Econ 300: Quantitative Methods in Economics. 11th Class 10/19/09
Econ 300: Quantitative Methods in Economics 11th Class 10/19/09 Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write. --H.G. Wells discuss test [do
Probability 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
Section 6.5. The Central Limit Theorem
Section 6.5 The Central Limit Theorem Idea Will allow us to combine the theory from 6.4 (sampling distribution idea) with our central limit theorem and that will allow us the do hypothesis testing in the
As you draw random samples of size n, as n increases, the sample means tend to be normally distributed.
The Central Limit Theorem The central limit theorem (clt for short) is one of the most powerful and useful ideas in all of statistics. The clt says that if we collect samples of size n with a "large enough
Chapter 6: The Normal Distribution
Chapter 6: The Normal Distribution Diana Pell Section 6.1: Normal Distributions Note: Recall that a continuous variable can assume all values between any two given values of the variables. Many continuous
Midterm 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
Class 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
Stat 213: Intro to Statistics 9 Central Limit Theorem
1 Stat 213: Intro to Statistics 9 Central Limit Theorem H. Kim Fall 2007 2 unknown parameters Example: A pollster is sure that the responses to his agree/disagree questions will follow a binomial distribution,
Chapter 6: The Normal Distribution
Chapter 6: The Normal Distribution Diana Pell Section 6.1: Normal Distributions Note: Recall that a continuous variable can assume all values between any two given values of the variables. Many continuous
MEMORIAL UNIVERSITY OF NEWFOUNDLAND DEPARTMENT OF MATHEMATICS AND STATISTICS MIDTERM EXAM - STATISTICS FALL 2014, SECTION 005
MEMORIAL UNIVERSITY OF NEWFOUNDLAND DEPARTMENT OF MATHEMATICS AND STATISTICS MIDTERM EXAM - STATISTICS 2550 - FALL 2014, SECTION 005 Instructor: A. Oyet Date: October 16, 2014 Name(Surname First): Student
Sampling 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
Chapter 4. The Normal Distribution
Chapter 4 The Normal Distribution 1 Chapter 4 Overview Introduction 4-1 Normal Distributions 4-2 Applications of the Normal Distribution 4-3 The Central Limit Theorem 4-4 The Normal Approximation to the
Math 140 Introductory Statistics
Math 140 Introductory Statistics Let s make our own sampling! If we use a random sample (a survey) or if we randomly assign treatments to subjects (an experiment) we can come up with proper, unbiased conclusions
Statistics 114 September 29, 2012
Statistics 114 September 29, 2012 Third Long Examination TGCapistrano I. TRUE OR FALSE. Write True if the statement is always true; otherwise, write False. 1. The fifth decile is equal to the 50 th percentile.
Week 1 Variables: Exploration, Familiarisation and Description. Descriptive Statistics.
Week 1 Variables: Exploration, Familiarisation and Description. Descriptive Statistics. Convergent validity: the degree to which results/evidence from different tests/sources, converge on the same conclusion.
Chapter 6.1 Confidence Intervals. Stat 226 Introduction to Business Statistics I. Chapter 6, Section 6.1
Stat 226 Introduction to Business Statistics I Spring 2009 Professor: Dr. Petrutza Caragea Section A Tuesdays and Thursdays 9:30-10:50 a.m. Chapter 6, Section 6.1 Confidence Intervals Confidence Intervals
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Chapter 6 Exam A Name The given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. 1) The probability of
Confidence Intervals Introduction
Confidence Intervals Introduction A point estimate provides no information about the precision and reliability of estimation. For example, the sample mean X is a point estimate of the population mean μ
Lecture 9 - Sampling Distributions and the CLT
Lecture 9 - Sampling Distributions and the CLT Sta102/BME102 Colin Rundel September 23, 2015 1 Variability of Estimates Activity Sampling distributions - via simulation Sampling distributions - via CLT
STAT 157 HW1 Solutions
STAT 157 HW1 Solutions http://www.stat.ucla.edu/~dinov/courses_students.dir/10/spring/stats157.dir/ Problem 1. 1.a: (6 points) Determine the Relative Frequency and the Cumulative Relative Frequency (fill