MAT140: Applied Statistical Methods Summary of Calculating Confidence Intervals and Sample Sizes for Estimating Parameters


 Jesse Wilkins
 2 years ago
 Views:
Transcription
1 MAT140: Applied Statistical Methods Summary of Calculating Confidence Intervals and Sample Sizes for Estimating Parameters Inferences about a population parameter can be made using sample statistics for the following: 1. Proportion (percentage of population that possesses some characteristic or trait) 2. Mean (average value of whatever quantity is being measured for the population) 3. Variance (NOT standard deviation, although variance is used to work with standard deviation) A confidence interval (CI) for one of the parameters listed above is generally constructed through the following process: 1. Determine the corresponding statistic from a sample 2. Determine the range of values (upper and lower bounds) assumed to contain the true value of the population parameter at the stated level of confidence It should be noted that although following the above procedure is the general process for making inferences about a population parameter based on a sample statistic, each of the three parameters for which valid inferences can be made has its own unique formulas to use. Furthermore, obtaining the range of values that is hoped to contain the true value of the actual population parameter does not guarantee that the true value of the population parameter actually falls in that range. Related to confidence intervals is the concept of determining the minimum sample size necessary to ensure valid results, which is done simply by solving the pertinent formula for where applicable. The following variables and abbreviations are used at various times when performing calculations related to confidence intervals and, later on, hypothesis testing (which is covered in a future chapter): = population proportion ( is the complement of ; and ) = population mean = population variance = population standard deviation = sample proportion ( is the complement of ; and ) = sample mean = sample variance = sample standard deviation = sample size = confidence interval = margin of error (used for calculating for or ) = complement of confidence level associated with (for example, a confidence level means, which means ) = area in each tail for a confidence interval ( represents the middle range of values) = critical value in normal distribution for for or with known value of = critical value in distribution for for with unknown value of = degrees of freedom ( ) = critical value in distribution for lower bound of for (or ) = critical value in distribution for upper bound of for (or )
2 Procedure for Estimating a Population Proportion b. The conditions for binomial distribution are satisfied: i. Fixed number of trials ( is set) ii. Trials are independent (the outcome of any one trial has no effect on any other trial) iii. Exactly two categories of outcomes for each trial (success and failure) iv. Probabilities remain constant for each trial ( and do not change) c. There are at least successes and failures (equivalent to and ) 2. If not provided, calculate the value of the sample proportion : (Note: 4. Look up the value of in the table of values for the normal distribution 5. Calculate the margin of error : 6. Calculate the limits and state the for the population proportion in one of the following ways: a. Preferred method: b. c. ( of ( and margin of error, simply solve the equation for above for : [ ] Notes: 1. It is highly unlikely that there will be prior knowledge to provide a value for. In such instances, it is customary to use (and, therefore, ) in the calculation for. (If prior knowledge provides a value of to be used, then that should be used instead.) 2. Always round the value of up to the next highest integer if the value is not an integer.
3 Procedure for Estimating a Population Mean When Is Known Note: In general, this procedure is not used since it would be extremely unlikely that a value for would be known without also knowing the true value of since the calculation of depends on the value of, although rare cases may exist; the more practical approach for estimating is outlined in the next section of this packet. b. The value of the population standard deviation is known c. Either or both of the following conditions are met: i. The population is normally distributed ii. The sample size 2. If not provided, calculate the value of the sample mean 4. Look up the value of in the table of values for the normal distribution 5. Calculate the margin of error : 6. Calculate the limits and state the for the population mean in one of the following ways: a. Preferred method: b. c. ( of ( and margin of error, simply solve the equation for above for : [ ] Note: Always round the value of up to the next highest integer if the value is not an integer.
4 Procedure for Estimating a Population Mean When Is Not Known b. Either or both of the following conditions are met: i. The population is normally distributed ii. The sample size 2. If not provided, calculate the value of the sample mean 3. If not provided, calculate the value of the sample standard deviation 4. Determine the value of based on the stated confidence level: 5. Determine the number of degrees of freedom, : 6. Look up the value of in the table of values for the distribution 7. Calculate the margin of error : 8. Calculate the limits and state the for the population mean in one of the following ways: a. Preferred method: b. c. ( of ( and margin of error, it is generally acceptable to simply solve the equation for above for and use the value in the row labeled Large for degrees of freedom as the value of (this is equivalent to the value of used in the formula from the previous section in which the population standard deviation is known): [ ] Notes: 1. If statistics from a sample of known size are provided, the value of from the row for the corresponding number of degrees of freedom can be used, resulting in a slightly larger minimum necessary sample size which will theoretically provide more accurate results. 2. To obtain the greatest minimum necessary sample size using this approach, the preceding formula can be used with degree of freedom, although the resulting sample size will be significantly larger and may not be practical when formally gathering data. 3. If the population cannot be assumed to be at least reasonably close to normally distributed, calculating a minimum sample size becomes complex beyond the scope of this course. 4. Always round the value of up to the next highest integer if the value is not an integer.
5 Procedure for Estimating a Population Variance b. The population must be normally distributed regardless of sample size 2. If not provided, calculate the value of the sample standard deviation 4. Determine the number of degrees of freedom, : 5. Look up the values of and in the table of values for the distribution 6. Calculate the limits and state the for the population variance : ( ( 7. If the for the population standard deviation is desired, simply take square roots: ( ( Because the distribution depends on the number of degrees of freedom, and the number of degrees of freedom depends on the sample size, it is not possible to determine the minimum sample size necessary to guarantee valid results for a stated confidence level of ( and margin of error by simply solving the equation for above for. However, complex procedures do exist to determine such sample sizes. Since those procedures are beyond the scope of this course, it is sufficient to simply note that Table 72 on page 376 of the textbook provides required minimum sample sizes for many of the most common confidence levels and margins of error. When necessary throughout this course, it is sufficient to simply look up a required minimum sample size in that table.
5.1 Identifying the Target Parameter
University of California, Davis Department of Statistics Summer Session II Statistics 13 August 20, 2012 Date of latest update: August 20 Lecture 5: Estimation with Confidence intervals 5.1 Identifying
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 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 informationReview. March 21, 2011. 155S7.1 2_3 Estimating a Population Proportion. Chapter 7 Estimates and Sample Sizes. Test 2 (Chapters 4, 5, & 6) Results
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 informationHow to Conduct a Hypothesis Test
How to Conduct a Hypothesis Test The idea of hypothesis testing is relatively straightforward. In various studies we observe certain events. We must ask, is the event due to chance alone, or is there some
More informationConfidence level. Most common choices are 90%, 95%, or 99%. (α = 10%), (α = 5%), (α = 1%)
Confidence Interval A confidence interval (or interval estimate) is a range (or an interval) of values used to estimate the true value of a population parameter. A confidence interval is sometimes abbreviated
More information3.4 Statistical inference for 2 populations based on two samples
3.4 Statistical inference for 2 populations based on two samples Tests for a difference between two population means The first sample will be denoted as X 1, X 2,..., X m. The second sample will be denoted
More informationChapter 8 Hypothesis Testing Chapter 8 Hypothesis Testing 81 Overview 82 Basics of Hypothesis Testing
Chapter 8 Hypothesis Testing 1 Chapter 8 Hypothesis Testing 81 Overview 82 Basics of Hypothesis Testing 83 Testing a Claim About a Proportion 85 Testing a Claim About a Mean: s Not Known 86 Testing
More informationStatistical 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 information2 Sample ttest (unequal sample sizes and unequal variances)
Variations of the ttest: Sample tail Sample ttest (unequal sample sizes and unequal variances) Like the last example, below we have ceramic sherd thickness measurements (in cm) of two samples representing
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 informationGrowingKnowing.com 2011
GrowingKnowing.com 2011 GrowingKnowing.com 2011 1 Estimates We are often asked to predict the future! When will you complete your team project? When will you make your first million dollars? When will
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 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 informationHYPOTHESIS TESTING: CONFIDENCE INTERVALS, TTESTS, ANOVAS, AND REGRESSION
HYPOTHESIS TESTING: CONFIDENCE INTERVALS, TTESTS, ANOVAS, AND REGRESSION HOD 2990 10 November 2010 Lecture Background This is a lightning speed summary of introductory statistical methods for senior undergraduate
More informationHypothesis Testing. Bluman Chapter 8
CHAPTER 8 Learning Objectives C H A P T E R E I G H T Hypothesis Testing 1 Outline 81 Steps in Traditional Method 82 z Test for a Mean 83 t Test for a Mean 84 z Test for a Proportion 85 2 Test for
More informationMeasuring the Power of a Test
Textbook Reference: Chapter 9.5 Measuring the Power of a Test An economic problem motivates the statement of a null and alternative hypothesis. For a numeric data set, a decision rule can lead to the rejection
More informationEstimation of the Mean and Proportion
1 Excel Manual Estimation of the Mean and Proportion Chapter 8 While the spreadsheet setups described in this guide may seem to be getting more complicated, once they are created (and tested!), they will
More informationChapter Study Guide. Chapter 11 Confidence Intervals and Hypothesis Testing for Means
OPRE504 Chapter Study Guide Chapter 11 Confidence Intervals and Hypothesis Testing for Means I. Calculate Probability for A Sample Mean When Population σ Is Known 1. First of all, we need to find out the
More informationTechnology StepbyStep Using StatCrunch
Technology StepbyStep Using StatCrunch Section 1.3 Simple Random Sampling 1. Select Data, highlight Simulate Data, then highlight Discrete Uniform. 2. Fill in the following window with the appropriate
More informationConfidence Intervals for the Difference Between Two Means
Chapter 47 Confidence Intervals for the Difference Between Two Means Introduction This procedure calculates the sample size necessary to achieve a specified distance from the difference in sample means
More informationMINITAB ASSISTANT WHITE PAPER
MINITAB ASSISTANT WHITE PAPER This paper explains the research conducted by Minitab statisticians to develop the methods and data checks used in the Assistant in Minitab 17 Statistical Software. OneWay
More informationConfidence Intervals for Cpk
Chapter 297 Confidence Intervals for Cpk Introduction This routine calculates the sample size needed to obtain a specified width of a Cpk confidence interval at a stated confidence level. Cpk is a process
More informationTHE FIRST SET OF EXAMPLES USE SUMMARY DATA... EXAMPLE 7.2, PAGE 227 DESCRIBES A PROBLEM AND A HYPOTHESIS TEST IS PERFORMED IN EXAMPLE 7.
THERE ARE TWO WAYS TO DO HYPOTHESIS TESTING WITH STATCRUNCH: WITH SUMMARY DATA (AS IN EXAMPLE 7.17, PAGE 236, IN ROSNER); WITH THE ORIGINAL DATA (AS IN EXAMPLE 8.5, PAGE 301 IN ROSNER THAT USES DATA FROM
More informationChapter 18 Combined Values Chart
Chapter 18 Combined Values Chart INTRODUCTION After impairment ratings have been obtained for all accepted conditions they must be combined to a single value known as the combined impairment rating. The
More informationTwoSample TTests Assuming Equal Variance (Enter Means)
Chapter 4 TwoSample TTests Assuming Equal Variance (Enter Means) Introduction This procedure provides sample size and power calculations for one or twosided twosample ttests when the variances of
More informationOdds ratio, Odds ratio test for independence, chisquared statistic.
Odds ratio, Odds ratio test for independence, chisquared statistic. Announcements: Assignment 5 is live on webpage. Due Wed Aug 1 at 4:30pm. (9 days, 1 hour, 58.5 minutes ) Final exam is Aug 9. Review
More informationTwoSample TTests Allowing Unequal Variance (Enter Difference)
Chapter 45 TwoSample TTests Allowing Unequal Variance (Enter Difference) Introduction This procedure provides sample size and power calculations for one or twosided twosample ttests when no assumption
More informationOneWay Analysis of Variance
OneWay Analysis of Variance Note: Much of the math here is tedious but straightforward. We ll skim over it in class but you should be sure to ask questions if you don t understand it. I. Overview A. We
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 informationLecture Notes Module 1
Lecture Notes Module 1 Study Populations A study population is a clearly defined collection of people, animals, plants, or objects. In psychological research, a study population usually consists of a specific
More informationHypothesis Testing Level I Quantitative Methods. IFT Notes for the CFA exam
Hypothesis Testing 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 3 2. Hypothesis Testing... 3 3. Hypothesis Tests Concerning the Mean... 10 4. Hypothesis Tests
More informationOneWay ANOVA using SPSS 11.0. SPSS ANOVA procedures found in the Compare Means analyses. Specifically, we demonstrate
1 OneWay ANOVA using SPSS 11.0 This section covers steps for testing the difference between three or more group means using the SPSS ANOVA procedures found in the Compare Means analyses. Specifically,
More information93.4 Likelihood ratio test. NeymanPearson lemma
93.4 Likelihood ratio test NeymanPearson lemma 91 Hypothesis Testing 91.1 Statistical Hypotheses Statistical hypothesis testing and confidence interval estimation of parameters are the fundamental
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 informationStats for Strategy Exam 1 InClass Practice Questions DIRECTIONS
Stats for Strategy Exam 1 InClass Practice Questions DIRECTIONS Choose the single best answer for each question. Discuss questions with classmates, TAs and Professor Whitten. Raise your hand to check
More informationSimple linear regression
Simple linear regression Introduction Simple linear regression is a statistical method for obtaining a formula to predict values of one variable from another where there is a causal relationship between
More informationMultipleComparison Procedures
MultipleComparison Procedures References A good review of many methods for both parametric and nonparametric multiple comparisons, planned and unplanned, and with some discussion of the philosophical
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 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 informationAdvanced Statistical Analysis of Mortality. Rhodes, Thomas E. and Freitas, Stephen A. MIB, Inc. 160 University Avenue. Westwood, MA 02090
Advanced Statistical Analysis of Mortality Rhodes, Thomas E. and Freitas, Stephen A. MIB, Inc 160 University Avenue Westwood, MA 02090 001(781)7516356 fax 001(781)3293379 trhodes@mib.com Abstract
More informationp ˆ (sample mean and sample
Chapter 6: Confidence Intervals and Hypothesis Testing When analyzing data, we can t just accept the sample mean or sample proportion as the official mean or proportion. When we estimate the statistics
More informationIntroduction to Stata
Introduction to Stata September 23, 2014 Stata is one of a few statistical analysis programs that social scientists use. Stata is in the midrange of how easy it is to use. Other options include SPSS,
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 informationSummary of Formulas and Concepts. Descriptive Statistics (Ch. 14)
Summary of Formulas and Concepts Descriptive Statistics (Ch. 14) Definitions Population: The complete set of numerical information on a particular quantity in which an investigator is interested. We assume
More informationNeed for Sampling. Very large populations Destructive testing Continuous production process
Chapter 4 Sampling and Estimation Need for Sampling Very large populations Destructive testing Continuous production process The objective of sampling is to draw a valid inference about a population. 4
More information7 Hypothesis testing  one sample tests
7 Hypothesis testing  one sample tests 7.1 Introduction Definition 7.1 A hypothesis is a statement about a population parameter. Example A hypothesis might be that the mean age of students taking MAS113X
More informationNull Hypothesis H 0. The null hypothesis (denoted by H 0
Hypothesis test In statistics, a hypothesis is a claim or statement about a property of a population. A hypothesis test (or test of significance) is a standard procedure for testing a claim about a property
More information, for x = 0, 1, 2, 3,... (4.1) (1 + 1/n) n = 2.71828... b x /x! = e b, x=0
Chapter 4 The Poisson Distribution 4.1 The Fish Distribution? The Poisson distribution is named after SimeonDenis Poisson (1781 1840). In addition, poisson is French for fish. In this chapter we will
More informationProbability Distributions
CHAPTER 5 Probability Distributions CHAPTER OUTLINE 5.1 Probability Distribution of a Discrete Random Variable 5.2 Mean and Standard Deviation of a Probability Distribution 5.3 The Binomial Distribution
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 informationHYPOTHESIS TESTING (ONE SAMPLE)  CHAPTER 7 1. used confidence intervals to answer questions such as...
HYPOTHESIS TESTING (ONE SAMPLE)  CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men
More informationCharacteristics of Binomial Distributions
Lesson2 Characteristics of Binomial Distributions In the last lesson, you constructed several binomial distributions, observed their shapes, and estimated their means and standard deviations. In Investigation
More informationIntroduction to Hypothesis Testing. Point estimation and confidence intervals are useful statistical inference procedures.
Introduction to Hypothesis Testing Point estimation and confidence intervals are useful statistical inference procedures. Another type of inference is used frequently used concerns tests of hypotheses.
More informationCHAPTER 11 CHISQUARE: NONPARAMETRIC COMPARISONS OF FREQUENCY
CHAPTER 11 CHISQUARE: NONPARAMETRIC COMPARISONS OF FREQUENCY The hypothesis testing statistics detailed thus far in this text have all been designed to allow comparison of the means of two or more samples
More informationChapter 5 Analysis of variance SPSS Analysis of variance
Chapter 5 Analysis of variance SPSS Analysis of variance Data file used: gss.sav How to get there: Analyze Compare Means Oneway ANOVA To test the null hypothesis that several population means are equal,
More informationCalculating PValues. Parkland College. Isela Guerra Parkland College. Recommended Citation
Parkland College A with Honors Projects Honors Program 2014 Calculating PValues Isela Guerra Parkland College Recommended Citation Guerra, Isela, "Calculating PValues" (2014). A with Honors Projects.
More informationindividualdifferences
1 Simple ANalysis Of Variance (ANOVA) Oftentimes we have more than two groups that we want to compare. The purpose of ANOVA is to allow us to compare group means from several independent samples. In general,
More informationChapter 8. Hypothesis Testing
Chapter 8 Hypothesis Testing Hypothesis In statistics, a hypothesis is a claim or statement about a property of a population. A hypothesis test (or test of significance) is a standard procedure for testing
More informationBasic Statistics. Probability and Confidence Intervals
Basic Statistics Probability and Confidence Intervals Probability and Confidence Intervals Learning Intentions Today we will understand: Interpreting the meaning of a confidence interval Calculating the
More informationMeans, standard deviations and. and standard errors
CHAPTER 4 Means, standard deviations and standard errors 4.1 Introduction Change of units 4.2 Mean, median and mode Coefficient of variation 4.3 Measures of variation 4.4 Calculating the mean and standard
More informationHypothesis Testing COMP 245 STATISTICS. Dr N A Heard. 1 Hypothesis Testing 2 1.1 Introduction... 2 1.2 Error Rates and Power of a Test...
Hypothesis Testing COMP 45 STATISTICS Dr N A Heard Contents 1 Hypothesis Testing 1.1 Introduction........................................ 1. Error Rates and Power of a Test.............................
More informationSurvey Process White Paper Series The Six Steps in Conducting Quantitative Marketing Research
Survey Process White Paper Series The Six Steps in Conducting Quantitative Marketing Research POLARIS MARKETING RESEARCH, INC. 1455 LINCOLN PARKWAY, SUITE 320 ATLANTA, GEORGIA 30346 404.816.0353 www.polarismr.com
More information1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96
1 Final Review 2 Review 2.1 CI 1propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years
More informationTesting Research and Statistical Hypotheses
Testing Research and Statistical Hypotheses Introduction In the last lab we analyzed metric artifact attributes such as thickness or width/thickness ratio. Those were continuous variables, which as you
More informationStudy Guide for the Final Exam
Study Guide for the Final Exam When studying, remember that the computational portion of the exam will only involve new material (covered after the second midterm), that material from Exam 1 will make
More informationFinal Exam Practice Problem Answers
Final Exam Practice Problem Answers The following data set consists of data gathered from 77 popular breakfast cereals. The variables in the data set are as follows: Brand: The brand name of the cereal
More informationHYPOTHESIS TESTING (ONE SAMPLE)  CHAPTER 7 1. used confidence intervals to answer questions such as...
HYPOTHESIS TESTING (ONE SAMPLE)  CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men
More informationIntroduction to Analysis of Variance (ANOVA) Limitations of the ttest
Introduction to Analysis of Variance (ANOVA) The Structural Model, The Summary Table, and the One Way ANOVA Limitations of the ttest Although the ttest is commonly used, it has limitations Can only
More informationMean = (sum of the values / the number of the value) if probabilities are equal
Population Mean Mean = (sum of the values / the number of the value) if probabilities are equal Compute the population mean Population/Sample mean: 1. Collect the data 2. sum all the values in the population/sample.
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 informationRegression Analysis: A Complete Example
Regression Analysis: A Complete Example This section works out an example that includes all the topics we have discussed so far in this chapter. A complete example of regression analysis. PhotoDisc, Inc./Getty
More informationRecall this chart that showed how most of our course would be organized:
Chapter 4 OneWay ANOVA Recall this chart that showed how most of our course would be organized: Explanatory Variable(s) Response Variable Methods Categorical Categorical Contingency Tables Categorical
More informationMathematics. Probability and Statistics Curriculum Guide. Revised 2010
Mathematics Probability and Statistics Curriculum Guide Revised 2010 This page is intentionally left blank. Introduction The Mathematics Curriculum Guide serves as a guide for teachers when planning instruction
More informationEstimation and Confidence Intervals
Estimation and Confidence Intervals Fall 2001 Professor Paul Glasserman B6014: Managerial Statistics 403 Uris Hall Properties of Point Estimates 1 We have already encountered two point estimators: th e
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 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 informationWhat Does the Correlation Coefficient Really Tell Us About the Individual?
What Does the Correlation Coefficient Really Tell Us About the Individual? R. C. Gardner and R. W. J. Neufeld Department of Psychology University of Western Ontario ABSTRACT The Pearson product moment
More informationIn this lesson you will learn to find zeros of polynomial functions that are not factorable.
2.6. Rational zeros of polynomial functions. In this lesson you will learn to find zeros of polynomial functions that are not factorable. REVIEW OF PREREQUISITE CONCEPTS: A polynomial of n th degree has
More information2 GENETIC DATA ANALYSIS
2.1 Strategies for learning genetics 2 GENETIC DATA ANALYSIS We will begin this lecture by discussing some strategies for learning genetics. Genetics is different from most other biology courses you have
More informationClass 19: Two Way Tables, Conditional Distributions, ChiSquare (Text: Sections 2.5; 9.1)
Spring 204 Class 9: Two Way Tables, Conditional Distributions, ChiSquare (Text: Sections 2.5; 9.) Big Picture: More than Two Samples In Chapter 7: We looked at quantitative variables and compared the
More informationCURVE FITTING LEAST SQUARES APPROXIMATION
CURVE FITTING LEAST SQUARES APPROXIMATION Data analysis and curve fitting: Imagine that we are studying a physical system involving two quantities: x and y Also suppose that we expect a linear relationship
More informationAP Statistics 2011 Scoring Guidelines
AP Statistics 2011 Scoring Guidelines The College Board The College Board is a notforprofit membership association whose mission is to connect students to college success and opportunity. Founded in
More informationTImath.com. F Distributions. Statistics
F Distributions ID: 9780 Time required 30 minutes Activity Overview In this activity, students study the characteristics of the F distribution and discuss why the distribution is not symmetric (skewed
More informationChapter 2. Hypothesis testing in one population
Chapter 2. Hypothesis testing in one population Contents Introduction, the null and alternative hypotheses Hypothesis testing process Type I and Type II errors, power Test statistic, level of significance
More informationCurriculum Map Statistics and Probability Honors (348) Saugus High School Saugus Public Schools 20092010
Curriculum Map Statistics and Probability Honors (348) Saugus High School Saugus Public Schools 20092010 Week 1 Week 2 14.0 Students organize and describe distributions of data by using a number of different
More informationSix Sigma: Sample Size Determination and Simple Design of Experiments
Six Sigma: Sample Size Determination and Simple Design of Experiments Short Examples Series using Risk Simulator For more information please visit: www.realoptionsvaluation.com or contact us at: admin@realoptionsvaluation.com
More informationWeek 3&4: Z tables and the Sampling Distribution of X
Week 3&4: Z tables and the Sampling Distribution of X 2 / 36 The Standard Normal Distribution, or Z Distribution, is the distribution of a random variable, Z N(0, 1 2 ). The distribution of any other normal
More informationA POPULATION MEAN, CONFIDENCE INTERVALS AND HYPOTHESIS TESTING
CHAPTER 5. A POPULATION MEAN, CONFIDENCE INTERVALS AND HYPOTHESIS TESTING 5.1 Concepts When a number of animals or plots are exposed to a certain treatment, we usually estimate the effect of the treatment
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 information2. DATA AND EXERCISES (Geos2911 students please read page 8)
2. DATA AND EXERCISES (Geos2911 students please read page 8) 2.1 Data set The data set available to you is an Excel spreadsheet file called cyclones.xls. The file consists of 3 sheets. Only the third is
More informationSample Paper for Research Methods. Daren H. Kaiser. Indiana University Purdue University Fort Wayne
Running head: RESEARCH METHODS PAPER 1 Sample Paper for Research Methods Daren H. Kaiser Indiana University Purdue University Fort Wayne Running head: RESEARCH METHODS PAPER 2 Abstract First notice that
More informationNonrandom/nonprobability sampling designs in quantitative research
206 RESEARCH MET HODOLOGY Nonrandom/nonprobability sampling designs in quantitative research N onprobability sampling designs do not follow the theory of probability in the choice of elements from the
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 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 informationEMPIRICAL FREQUENCY DISTRIBUTION
INTRODUCTION TO MEDICAL STATISTICS: Mirjana Kujundžić Tiljak EMPIRICAL FREQUENCY DISTRIBUTION observed data DISTRIBUTION  described by mathematical models 2 1 when some empirical distribution approximates
More informationPsyc 250 Statistics & Experimental Design. Single & Paired Samples ttests
Psyc 250 Statistics & Experimental Design Single & Paired Samples ttests Part 1 Data Entry For any statistical analysis with any computer program, it is always important that data are entered correctly
More informationSTRUTS: Statistical Rules of Thumb. Seattle, WA
STRUTS: Statistical Rules of Thumb Gerald van Belle Departments of Environmental Health and Biostatistics University ofwashington Seattle, WA 981954691 Steven P. Millard Probability, Statistics and Information
More informationIndependent t Test (Comparing Two Means)
Independent t Test (Comparing Two Means) The objectives of this lesson are to learn: the definition/purpose of independent ttest when to use the independent ttest the use of SPSS to complete an independent
More information