Constructing and Interpreting Confidence Intervals


 Nicholas Long
 2 years ago
 Views:
Transcription
1 Constructing and Interpreting Confidence Intervals
2 Confidence Intervals In this power point, you will learn: Why confidence intervals are important in evaluation research How to interpret a confidence interval How to construct a confidence interval yourself
3 Confidence Intervals Purpose The purpose of a confidence interval is to estimate a population mean or proportion based on a sample mean or proportion. Relationship with Margin of Error When estimating the population mean or proportion, we do not try to estimate the exact value. We construct an interval within which we are 95% sure the population means or proportion lies. The width of the interval on each side of the mean or proportion is referred to as the margin of error. Example.If you estimate that the percent of farmers who will increase crop yield using the new fertilizer is 75% and the margin of error is 5%, more technically you are stating that you are 95% sure the population percent is somewhere between 70% and 80%. Example using a Mean..If you estimate the mean number of bushels of corn to be 400 for farmers who used the new fertilizer and our margin of error is 10, then you are stating you are 95% sure the mean is somewhere between 390 to 410.
4 Constructing a Confidence Interval Constructing a confidence interval by hand Before you can construct a confidence interval by hand, you must have data from a random sample. You need: The sample size The proportion or mean you want to estimate The standard deviation of the mean you want to estimate A critical value associated with the probability For a proportion this is a Z value The value associated with a 95% confidence interval is 1.96 Other values can be found in a Z table For a mean this is a T value The value associated with a 95% confidence interval is 1.98 Other values can be found in a T table
5 Constructing a Confidence Interval It is relatively easy to construct a confidence interval. The following slides tell you how to: Construct a confidence interval using a proportion or percent Statistical formula (most precise) Formula used by OpinionPolls (most commonly used) Simplified formula used by OpinionPolls (easiest and most conservative) Construct a confidence interval using a mean
6
7
8 EXAMPLE of Confidence Interval for a Proportion 50% of our sample of 36 individuals indicated they would vote for Obama in this election. Research Question: What percent of population will vote for Obama? Relevant Information p =.50 n = 36 z = 1.96 for 95% confidence interval Simple Instructions 1.96 times the square root of.50 (1 .50) divided by 36 (number of class members who voted) Take this number and add it to.50 and then subtract it from.50 (proportion who voted for Obama in sample) Or Step by Step 34 to 66% of the population will vote Step =.50 for Obama. NOTE, Step 2.50 times.50 =.25 our confidence Step 3.25 divided by 36 (n) = interval is so wide primarily because Step 4 Square root of = our sample is so Step times = small. Step 6.50 plus = Step 7.50 minus = Step 8 Confidence interval is to.66333
9 We are 95% sure that the mean score is between 73.1 and 78.5.
10 Example of Confidence Interval for a Mean Research Question What is the mean GPA of participants after participating in our tutoring program? Relevant Information Sample GPA = Sample Size = 40 T Value = 1.98 (value for a 95% confidence interval.) Standard Deviation of sample =.1864 Step by Step Instructions Step times.1864=.3691 Step 2 Square root of 40 = Step /6.3246=.0584 Step plus.0584= Step minus.0584= Conclusion: We are 95% sure that the mean GPA for our entire group is between
11 Width of Confidence Intervals Factors that influence the width of the interval: Standard Error Standard error estimates the dispersion of the data in the population. The more dispersed your data the wider is your confidence interval.* Sample Size The smaller the sample size that you used to construct a confidence interval then the wider the confidence interval. In layman s terms, you can estimate a population mean or proportion more accurately if you have a larger sample size. Probability The greater the probability, the wider will be your confidence interval.** Thus a 99% confidence interval is wider than a 95% confidence interval. In layman s terms, the more certain you want to be that the proportion or mean actually does lie within the interval the wider the interval must be. Proportion as a Special Case When estimating a proportion then the closer to the middle (.5) the proportion is the wider will be your confidence interval. *The margin of error is directly related to the width of the confidence interval. The wider the interval, the greater the margin of error. **Rule of thumb is to use a 95% confidence interval, but you can construct an interval with any degree of certainty.
12 Contact Information Dr. Carol Albrecht USU Extension Assessment Specialist
Statistical Inference
Statistical Inference Idea: Estimate parameters of the population distribution using data. How: Use the sampling distribution of sample statistics and methods based on what would happen if we used this
More informationGraphing Data Presentation of Data in Visual Forms
Graphing Data Presentation of Data in Visual Forms Purpose of Graphing Data Audience Appeal Provides a visually appealing and succinct representation of data and summary statistics Provides a visually
More informationInferential Statistics. What are they? When would you use them?
Inferential Statistics What are they? When would you use them? What are inferential statistics? Why learn about inferential statistics? Why use inferential statistics? When are inferential statistics utilized?
More informationResearch Methods 1 Handouts, Graham Hole,COGS  version 1.0, September 2000: Page 1:
Research Methods 1 Handouts, Graham Hole,COGS  version 1.0, September 2000: Page 1: THE NORMAL CURVE AND "Z" SCORES: The Normal Curve: The "Normal" curve is a mathematical abstraction which conveniently
More informationWeek 4: Standard Error and Confidence Intervals
Health Sciences M.Sc. Programme Applied Biostatistics Week 4: Standard Error and Confidence Intervals Sampling Most research data come from subjects we think of as samples drawn from a larger population.
More informationCALCULATIONS & STATISTICS
CALCULATIONS & STATISTICS CALCULATION OF SCORES Conversion of 15 scale to 0100 scores When you look at your report, you will notice that the scores are reported on a 0100 scale, even though respondents
More informationAP * Statistics Review
AP * Statistics Review Confidence Intervals Teacher Packet AP* is a trademark of the College Entrance Examination Board. The College Entrance Examination Board was not involved in the production of this
More informationUSING SAMPLING TO ASSESS LIBRARY COLLECTIONS
USING SAMPLING TO ASSESS LIBRARY COLLECTIONS by Jim Self Director, Management Information Services University of Virginia Library December 2001 self@virginia.edu This document is designed to demonstrate
More informationInferential Statistics
Inferential Statistics Sampling and the normal distribution Zscores Confidence levels and intervals Hypothesis testing Commonly used statistical methods Inferential Statistics Descriptive statistics are
More informationAn interval estimate (confidence interval) is an interval, or range of values, used to estimate a population parameter. For example 0.476<p<0.
Lecture #7 Chapter 7: Estimates and sample sizes In this chapter, we will learn an important technique of statistical inference to use sample statistics to estimate the value of an unknown population parameter.
More informationProb & Stats. Chapter 9 Review
Chapter 9 Review Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally
More informationName: Date: Use the following to answer questions 34:
Name: Date: 1. Determine whether each of the following statements is true or false. A) The margin of error for a 95% confidence interval for the mean increases as the sample size increases. B) The margin
More information103 Measures of Central Tendency and Variation
103 Measures of Central Tendency and Variation So far, we have discussed some graphical methods of data description. Now, we will investigate how statements of central tendency and variation can be used.
More informationStatistical Intervals. Chapter 7 Stat 4570/5570 Material from Devore s book (Ed 8), and Cengage
7 Statistical Intervals Chapter 7 Stat 4570/5570 Material from Devore s book (Ed 8), and Cengage Confidence Intervals The CLT tells us that as the sample size n increases, the sample mean X is close to
More informationSampling (cont d) and Confidence Intervals Lecture 9 8 March 2006 R. Ryznar
Sampling (cont d) and Confidence Intervals 11.220 Lecture 9 8 March 2006 R. Ryznar Census Surveys Decennial Census Every (over 11 million) household gets the short form and 17% or 1/6 get the long form
More informationCONFIDENCE INTERVALS I
CONFIDENCE INTERVALS I ESTIMATION: the sample mean Gx is an estimate of the population mean µ point of sampling is to obtain estimates of population values Example: for 55 students in Section 105, 45 of
More informationSimple Regression Theory II 2010 Samuel L. Baker
SIMPLE REGRESSION THEORY II 1 Simple Regression Theory II 2010 Samuel L. Baker Assessing how good the regression equation is likely to be Assignment 1A gets into drawing inferences about how close the
More informationAP STATISTICS 2011 SCORING GUIDELINES (Form B)
AP STATISTICS 2011 SCORING GUIDELINES (Form B) Question 5 Intent of Question The primary goals of this question were to assess students ability to (1) identify and check appropriate conditions for inference;
More informationSample Size Determination
Sample Size Determination Population A: 10,000 Population B: 5,000 Sample 10% Sample 15% Sample size 1000 Sample size 750 The process of obtaining information from a subset (sample) of a larger group (population)
More informationLess Stress More Success Maths Leaving Cert Higher Level Paper 2
Less Stress More Success Maths Leaving Cert Higher Level Paper 2 Revised pages for Chapter 13 Statistics IV: The Normal Curve, z Scores, Hypothesis Testing and Simulation 228 LESS STRESS MORE SUCCESS
More informationBA 275 Review Problems  Week 5 (10/23/0610/27/06) CD Lessons: 48, 49, 50, 51, 52 Textbook: pp. 380394
BA 275 Review Problems  Week 5 (10/23/0610/27/06) CD Lessons: 48, 49, 50, 51, 52 Textbook: pp. 380394 1. Does vigorous exercise affect concentration? In general, the time needed for people to complete
More information6.4 Normal Distribution
Contents 6.4 Normal Distribution....................... 381 6.4.1 Characteristics of the Normal Distribution....... 381 6.4.2 The Standardized Normal Distribution......... 385 6.4.3 Meaning of Areas under
More informationConfidence Intervals for One Standard Deviation Using Standard Deviation
Chapter 640 Confidence Intervals for One Standard Deviation Using Standard Deviation Introduction This routine calculates the sample size necessary to achieve a specified interval width or distance from
More informationConfidence Intervals about a Population Mean
Confidence Intervals about a Population Mean MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2015 Motivation Goal: to estimate a population mean µ based on data collected
More informationContent Sheet 71: Overview of Quality Control for Quantitative Tests
Content Sheet 71: Overview of Quality Control for Quantitative Tests Role in quality management system Quality Control (QC) is a component of process control, and is a major element of the quality management
More informationContingency Tables and the Chi Square Statistic. Interpreting Computer Printouts and Constructing Tables
Contingency Tables and the Chi Square Statistic Interpreting Computer Printouts and Constructing Tables Contingency Tables/Chi Square Statistics What are they? A contingency table is a table that shows
More informationPoint and Interval Estimates
Point and Interval Estimates Suppose we want to estimate a parameter, such as p or µ, based on a finite sample of data. There are two main methods: 1. Point estimate: Summarize the sample by a single number
More informationSocial Studies 201 Notes for November 19, 2003
1 Social Studies 201 Notes for November 19, 2003 Determining sample size for estimation of a population proportion Section 8.6.2, p. 541. As indicated in the notes for November 17, when sample size is
More informationSolution: There are TWO square roots of 196, a positive number and a negative number. So, since and 14 2
5.7 Introduction to Square Roots The Square of a Number The number x is called the square of the number x. EX) 9 9 9 81, the number 81 is the square of the number 9. 4 4 4 16, the number 16 is the square
More informationRegression Analysis: Basic Concepts
The simple linear model Regression Analysis: Basic Concepts Allin Cottrell Represents the dependent variable, y i, as a linear function of one independent variable, x i, subject to a random disturbance
More informationStatistical Confidence Calculations
Statistical Confidence Calculations Statistical Methodology Omniture Test&Target utilizes standard statistics to calculate confidence, confidence intervals, and lift for each campaign. The student s T
More informationExperimental Design. Power and Sample Size Determination. Proportions. Proportions. Confidence Interval for p. The Binomial Test
Experimental Design Power and Sample Size Determination Bret Hanlon and Bret Larget Department of Statistics University of Wisconsin Madison November 3 8, 2011 To this point in the semester, we have largely
More informationPrediction and Confidence Intervals in Regression
Fall Semester, 2001 Statistics 621 Lecture 3 Robert Stine 1 Prediction and Confidence Intervals in Regression Preliminaries Teaching assistants See them in Room 3009 SHDH. Hours are detailed in the syllabus.
More informationGood luck! BUSINESS STATISTICS FINAL EXAM INSTRUCTIONS. Name:
Glo bal Leadership M BA BUSINESS STATISTICS FINAL EXAM Name: INSTRUCTIONS 1. Do not open this exam until instructed to do so. 2. Be sure to fill in your name before starting the exam. 3. You have two hours
More informationPower and Sample Size Determination
Power and Sample Size Determination Bret Hanlon and Bret Larget Department of Statistics University of Wisconsin Madison November 3 8, 2011 Power 1 / 31 Experimental Design To this point in the semester,
More informationSampling Distribution of a Sample Proportion
Sampling Distribution of a Sample Proportion From earlier material remember that if X is the count of successes in a sample of n trials of a binomial random variable then the proportion of success is given
More informationSimple Linear Regression
STAT 101 Dr. Kari Lock Morgan Simple Linear Regression SECTIONS 9.3 Confidence and prediction intervals (9.3) Conditions for inference (9.1) Want More Stats??? If you have enjoyed learning how to analyze
More informationUnit 26 Estimation with Confidence Intervals
Unit 26 Estimation with Confidence Intervals Objectives: To see how confidence intervals are used to estimate a population proportion, a population mean, a difference in population proportions, or a difference
More informationAn Introduction to Sampling
An Introduction to Sampling Sampling is the process of selecting a subset of units from the population. We use sampling formulas to determine how many to select because it is based on the characteristics
More information4. Continuous Random Variables, the Pareto and Normal Distributions
4. Continuous Random Variables, the Pareto and Normal Distributions A continuous random variable X can take any value in a given range (e.g. height, weight, age). The distribution of a continuous random
More informationLesson 1: Comparison of Population Means Part c: Comparison of Two Means
Lesson : Comparison of Population Means Part c: Comparison of Two Means Welcome to lesson c. This third lesson of lesson will discuss hypothesis testing for two independent means. Steps in Hypothesis
More informationSAMPLING DISTRIBUTIONS
0009T_c07_308352.qd 06/03/03 20:44 Page 308 7Chapter SAMPLING DISTRIBUTIONS 7.1 Population and Sampling Distributions 7.2 Sampling and Nonsampling Errors 7.3 Mean and Standard Deviation of 7.4 Shape of
More informationProbability and Statistics Prof. Dr. Somesh Kumar Department of Mathematics Indian Institute of Technology, Kharagpur
Probability and Statistics Prof. Dr. Somesh Kumar Department of Mathematics Indian Institute of Technology, Kharagpur Module No. #01 Lecture No. #15 Special DistributionsVI Today, I am going to introduce
More informationSampling Distributions and the Central Limit Theorem
135 Part 2 / Basic Tools of Research: Sampling, Measurement, Distributions, and Descriptive Statistics Chapter 10 Sampling Distributions and the Central Limit Theorem In the previous chapter we explained
More informationNormal distribution. ) 2 /2σ. 2π σ
Normal distribution The normal distribution is the most widely known and used of all distributions. Because the normal distribution approximates many natural phenomena so well, it has developed into a
More informationOnline Resource 6. Estimating the required sample size
Online Resource 6. Estimating the required sample size Power calculations help program managers and evaluators estimate the required sample size that is large enough to provide sufficient statistical power
More informationUnit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression
Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Objectives: To perform a hypothesis test concerning the slope of a least squares line To recognize that testing for a
More informationCONFIDENCE INTERVALS ON µ WHEN σ IS UNKNOWN
CONFIDENCE INTERVALS ON µ WHEN σ IS UNKNOWN A. Introduction 1. this situation, where we do not know anything about the population but the sample characteristics, is far and away the most common circumstance
More informationBIOSTATISTICS QUIZ ANSWERS
BIOSTATISTICS QUIZ ANSWERS 1. When you read scientific literature, do you know whether the statistical tests that were used were appropriate and why they were used? a. Always b. Mostly c. Rarely d. Never
More informationConversions between percents, decimals, and fractions
Click on the links below to jump directly to the relevant section Conversions between percents, decimals and fractions Operations with percents Percentage of a number Percent change Conversions between
More informationNET PRESENT VALUE SIMULATING WITH A SPREADSHEET
Journal of Defense Resources Management No. 1 (1) / 2010 NET PRESENT VALUE SIMULATING WITH A SPREADSHEET Maria CONSTANTINESCU Regional Department of Defense Resources Management Studies Abstract: Decision
More informationLet m denote the margin of error. Then
S:105 Statistical Methods and Computing Sample size for confidence intervals with σ known t Intervals Lecture 13 Mar. 6, 009 Kate Cowles 374 SH, 335077 kcowles@stat.uiowa.edu 1 The margin of error The
More informationfind confidence interval for a population mean when the population standard deviation is KNOWN Understand the new distribution the tdistribution
Section 8.3 1 Estimating a Population Mean Topics find confidence interval for a population mean when the population standard deviation is KNOWN find confidence interval for a population mean when the
More informationChapter 3: Data Description Numerical Methods
Chapter 3: Data Description Numerical Methods Learning Objectives Upon successful completion of Chapter 3, you will be able to: Summarize data using measures of central tendency, such as the mean, median,
More informationSummary of Probability
Summary of Probability Mathematical Physics I Rules of Probability The probability of an event is called P(A), which is a positive number less than or equal to 1. The total probability for all possible
More informationFixedEffect Versus RandomEffects Models
CHAPTER 13 FixedEffect Versus RandomEffects Models Introduction Definition of a summary effect Estimating the summary effect Extreme effect size in a large study or a small study Confidence interval
More informationvariable univariate data measure of central tendency parameter statistic margin of sampling error measure of variation variance standard deviation
variable univariate data measure of central tendency parameter statistic margin of sampling error measure of variation variance standard deviation Measures of Central Tendency A. SALARIES A new Internet
More informationChapter 7. Estimates and Sample Size
Chapter 7. Estimates and Sample Size Chapter Problem: How do we interpret a poll about global warming? Pew Research Center Poll: From what you ve read and heard, is there a solid evidence that the average
More informationUnderstanding Variability
3 Vive la Différence Understanding Variability Difficulty Scale (moderately easy, but not a cinch) How much Excel? (a ton) What you ll learn about in this chapter Why variability is valuable as a descriptive
More informationBiostatistics: DESCRIPTIVE STATISTICS: 2, VARIABILITY
Biostatistics: DESCRIPTIVE STATISTICS: 2, VARIABILITY 1. Introduction Besides arriving at an appropriate expression of an average or consensus value for observations of a population, it is important to
More informationConfidence Intervals for Cp
Chapter 296 Confidence Intervals for Cp Introduction This routine calculates the sample size needed to obtain a specified width of a Cp confidence interval at a stated confidence level. Cp is a process
More informationRevenue and Costs for Corn, Soybeans, Wheat, and DoubleCrop Soybeans, Actual for 2009 through 2015, Projected 2016
CROP COSTS Department of Agricultural and Consumer Economics University of Illinois Revenue and Costs for Corn, Soybeans, Wheat, and DoubleCrop Soybeans, Actual for 2009 through 2015, Projected 2016 Department
More informationSample Size Issues for Conjoint Analysis
Chapter 7 Sample Size Issues for Conjoint Analysis I m about to conduct a conjoint analysis study. How large a sample size do I need? What will be the margin of error of my estimates if I use a sample
More information28: Square Roots and Real Numbers. 28: Square Roots and Real Numbers
OBJECTIVE: You must be able to find a square root, classify numbers, and graph solution of inequalities on number lines. square root  one of two equal factors of a number A number that will multiply by
More informationLAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING
LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING In this lab you will explore the concept of a confidence interval and hypothesis testing through a simulation problem in engineering setting.
More informationChapter 7  Practice Problems 1
Chapter 7  Practice Problems 1 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) Define a point estimate. What is the
More informationFarm Business Survey  Statistical information
Farm Business Survey  Statistical information Sample representation and design The sample structure of the FBS was redesigned starting from the 2010/11 accounting year. The coverage of the survey is
More informationCOMP6053 lecture: Relationship between two variables: correlation, covariance and rsquared. jn2@ecs.soton.ac.uk
COMP6053 lecture: Relationship between two variables: correlation, covariance and rsquared jn2@ecs.soton.ac.uk Relationships between variables So far we have looked at ways of characterizing the distribution
More informationMEASURES OF VARIATION
NORMAL DISTRIBTIONS MEASURES OF VARIATION In statistics, it is important to measure the spread of data. A simple way to measure spread is to find the range. But statisticians want to know if the data are
More information5.4 The Quadratic Formula
Section 5.4 The Quadratic Formula 481 5.4 The Quadratic Formula Consider the general quadratic function f(x) = ax + bx + c. In the previous section, we learned that we can find the zeros of this function
More informationData Analysis: Describing Data  Descriptive Statistics
WHAT IT IS Return to Table of ontents Descriptive statistics include the numbers, tables, charts, and graphs used to describe, organize, summarize, and present raw data. Descriptive statistics are most
More informationSolutions 7. Review, one sample ttest, independent twosample ttest, binomial distribution, standard errors and onesample proportions.
Solutions 7 Review, one sample ttest, independent twosample ttest, binomial distribution, standard errors and onesample proportions. (1) Here we debunk a popular misconception about confidence intervals
More informationStandard Deviation Calculator
CSS.com Chapter 35 Standard Deviation Calculator Introduction The is a tool to calculate the standard deviation from the data, the standard error, the range, percentiles, the COV, confidence limits, or
More information4. Introduction to Statistics
Statistics for Engineers 41 4. Introduction to Statistics Descriptive Statistics Types of data A variate or random variable is a quantity or attribute whose value may vary from one unit of investigation
More informationMATH 10: Elementary Statistics and Probability Chapter 7: The Central Limit Theorem
MATH 10: Elementary Statistics and Probability Chapter 7: The Central Limit Theorem Tony Pourmohamad Department of Mathematics De Anza College Spring 2015 Objectives By the end of this set of slides, you
More informationHow to Construct a Seasonal Index
How to Construct a Seasonal Index Methods of Constructing a Seasonal Index There are several ways to construct a seasonal index. The simplest is to produce a graph with the factor being studied (i.e.,
More informationUDOFIA ITON UDOFIA EDET E. NKEREUWEM Library Department University of Calabar Calabar Nigeria
Annals of Library Science and Documentation 42,3; 1995; 96100. SAMPLE SIZE DETERMINATION: A COMPARISON OF ATTRIBUTE AND CONTINUOUS VARIABLE METHODS UDOFIA ITON UDOFIA EDET E. NKEREUWEM Library Department
More informationExperimental Errors and Uncertainty
Experimental Errors and Uncertainty No physical quantity can be measured with perfect certainty; there are always errors in any measurement. This means that if we measure some quantity and, then, repeat
More informationThe Sampling Distribution of the Mean Confidence Intervals for a Proportion
Math 130 Jeff Stratton Name The Sampling Distribution of the Mean Confidence Intervals for a Proportion Goal: To gain experience with the sampling distribution of the mean, and with confidence intervals
More informationDETERMINING SURVEY SAMPLE SIZE A SIMPLE PLAN
DETERMINING SURVEY SAMPLE SIZE A SIMPLE PLAN Prepared by Market Directions Market Directions B O S T O N 6173231862 8004759808 www.marketdirectionsmr.com info@marketdirectionsmr.com DETERMING SAMPLE
More informationDescriptive Statistics
Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize
More informationA Summary of Error Propagation
A Summary of Error Propagation Suppose you measure some quantities a, b, c,... with uncertainties δa, δb, δc,.... Now you want to calculate some other quantity Q which depends on a and b and so forth.
More informationIntroduction to Hypothesis Testing
I. Terms, Concepts. Introduction to Hypothesis Testing A. In general, we do not know the true value of population parameters  they must be estimated. However, we do have hypotheses about what the true
More informationHence, multiplying by 12, the 95% interval for the hourly rate is (965, 1435)
Confidence Intervals for Poisson data For an observation from a Poisson distribution, we have σ 2 = λ. If we observe r events, then our estimate ˆλ = r : N(λ, λ) If r is bigger than 20, we can use this
More informationStandard Deviation Estimator
CSS.com Chapter 905 Standard Deviation Estimator Introduction Even though it is not of primary interest, an estimate of the standard deviation (SD) is needed when calculating the power or sample size of
More informationHOSPITALITY Math Assessment Preparation Guide. Introduction Operations with Whole Numbers Operations with Integers 9
HOSPITALITY Math Assessment Preparation Guide Please note that the guide is for reference only and that it does not represent an exact match with the assessment content. The Assessment Centre at George
More informationReport of for Chapter 2 pretest
Report of for Chapter 2 pretest Exam: Chapter 2 pretest Category: Organizing and Graphing Data 1. "For our study of driving habits, we recorded the speed of every fifth vehicle on Drury Lane. Nearly every
More information1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number
1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x  x) B. x 3 x C. 3x  x D. x  3x 2) Write the following as an algebraic expression
More informationMEASURES OF DISPERSION
MEASURES OF DISPERSION Measures of Dispersion While measures of central tendency indicate what value of a variable is (in one sense or other) average or central or typical in a set of data, measures of
More informationMind on Statistics. Chapter 10
Mind on Statistics Chapter 10 Section 10.1 Questions 1 to 4: Some statistical procedures move from population to sample; some move from sample to population. For each of the following procedures, determine
More informationComments 2 For Discussion Sheet 2 and Worksheet 2 Frequency Distributions and Histograms
Comments 2 For Discussion Sheet 2 and Worksheet 2 Frequency Distributions and Histograms Discussion Sheet 2 We have studied graphs (charts) used to represent categorical data. We now want to look at a
More informationOutline. 1 Confidence Intervals for Proportions. 2 Sample Sizes for Proportions. 3 Student s tdistribution. 4 Confidence Intervals without σ
Outline 1 Confidence Intervals for Proportions 2 Sample Sizes for Proportions 3 Student s tdistribution 4 Confidence Intervals without σ Outline 1 Confidence Intervals for Proportions 2 Sample Sizes for
More informationThe Philosophy of Hypothesis Testing, Questions and Answers 2006 Samuel L. Baker
HYPOTHESIS TESTING PHILOSOPHY 1 The Philosophy of Hypothesis Testing, Questions and Answers 2006 Samuel L. Baker Question: So I'm hypothesis testing. What's the hypothesis I'm testing? Answer: When you're
More informationSample Size Determination Using Statgraphics Centurion
Sample Size Determination Using Statgraphics Centurion Neil W. Polhemus, CTO, StatPoint Technologies, Inc. Copyright 2012 by StatPoint Technologies, Inc. Web site: www.statgraphics.com Preliminaries One
More informationStat 20: Intro to Probability and Statistics
Stat 20: Intro to Probability and Statistics Lecture 16: More Box Models Tessa L. ChildersDay UC Berkeley 22 July 2014 By the end of this lecture... You will be able to: Determine what we expect the sum
More information! x sum of the entries
3.1 Measures of Central Tendency (Page 1 of 16) 3.1 Measures of Central Tendency Mean, Median and Mode! x sum of the entries a. mean, x = = n number of entries Example 1 Find the mean of 26, 18, 12, 31,
More informationThe factor of safety is a factor of ignorance. If the stress on a part at a critical location (the
Appendix C The Factor of Safety as a Design Variable C.1 INTRODUCTION The factor of safety is a factor of ignorance. If the stress on a part at a critical location (the applied stress) is known precisely,
More informationELEMENTARY PROBABILITY
ELEMENTARY PROBABILITY Events and event sets. Consider tossing a die. There are six possible outcomes, which we shall denote by elements of the set {A i ; i =1, 2,...,6}. A numerical value is assigned
More informationThe Math. P (x) = 5! = 1 2 3 4 5 = 120.
The Math Suppose there are n experiments, and the probability that someone gets the right answer on any given experiment is p. So in the first example above, n = 5 and p = 0.2. Let X be the number of correct
More informationNumerical Measures of Central Tendency
Numerical Measures of Central Tendency Often, it is useful to have special numbers which summarize characteristics of a data set These numbers are called descriptive statistics or summary statistics. A
More information