indicate how accurate the is and how we are that the result is correct. We use intervals for this purpose.


 Myrtle Shelton
 1 years ago
 Views:
Transcription
1 Sect. 6.1: Confidence Intervals Statistical Confidence When we calculate an, say, of the population parameter, we want to indicate how accurate the is and how we are that the result is correct. We use intervals for this purpose. Eample: SAT Scores Suppose the entire population of SAT scores has mean and standard deviation. If we repeatedly sampled 500 scores from this population, then the sample mean,, follows the Normal(, ) distribution. Assume we know the value of is 100. Then, = 1) Using the rule, we know that will fall within 2 with probability. of the population mean 2) In our case, 2 =. To say that lies within 9 points of saying that is within points of. is equivalent to Combining these two facts we can state % of all samples (of size n = 500) will capture the true value of in the interval  to +. We can rewrite this interval as. Eample cont d Suppose our sample mean was 450. Then we say that we are % confident that the unknown mean score lies in the interval (, ) = (, ). 1 Sta 245 Sec 6.1 SB
2 Remember, we don t know for sure if this interval contains sampling gives correct results % of the time.! We just know that this method of Confidence Intervals This interval we just calculated is called a % interval. In general, intervals for a parameter consist of two parts: 1) An interval calculated from the data of the form estimate The conveys how accurate we believe our guess of the true parameter value is, based on the variability of the estimate. 2) A C, which gives the that the interval captures the true parameter value in repeated samples. Many types of intervals eist for various kinds of parameters. We will concentrate on intervals for the mean of a population. Intervals for a Population Mean Choose a SRS of size n from a population having unknown mean deviation. A level C interval for is and known standard Here, is the value on the standard normal curve with area C between  and. The interval is eact when the original population distribution is normal and is approimately correct for large otherwise. 2 Sta 245 Sec 6.1 SB
3 The most commonly used intervals are C 90% 95% 99% Values of for other values of C can be found using the bottom 2 rows of Table. Eample: SAT Scores Suppose we want to find an 80% confidence interval for the mean SAT score. Recall the population distribution was Normal(, = 100) and our sample mean was = 450. Behavior of Confidence Intervals What happens to the margin of error when sample size increases? Does it increase, decrease or stay the same? How does this affect the size of the resulting confidence interval? What happens to the size of the confidence interval as we decrease the confidence level C? (Hint: what happens to the value of?) How does the size of affect the margin of error? Thus we have 3 ways of reducing the size of the confidence interval: 1) 2) 3) 3 Sta 245 Sec 6.1 SB
4 Eample A randomized comparative eperiment studied the effect of diet on blood pressure. Researchers divided 54 healthy white males at random into two groups. One group received a calcium supplement and the other a placebo. Prior to the study, the seated systolic blood pressure was measured. The mean and standard deviation of the measurements for 27 members of the placebo group was reported to be = and s = 9.3. We want to get an idea of what the mean,, is for the blood pressure of the population from which the subjects were recruited. Calculate a 68 for. Q: Is it necessary to assume the population of systolic blood pressure measurements is normal? Q: What important assumption is required for the confidence interval to be valid? Choosing the Sample Size When designing a study, part of the preparation involves deciding the subjects necessary. Usually researchers will have a desired level and error they want to attain. Let m represent the error. For the sample mean recall we have m We can substitute values for m, and determine n is n and then solve for n. The resulting formula to *****Always round your answer!!***** Eample: SAT Scores Suppose we want to estimate the true mean SAT score to within 6 points with 95% confidence. What sample size do we need? 4 Sta 245 Sec 6.1 SB
5 CAUTIONS WARNINGS: How the data was collected is important!! There is no correct method for inference from data with bias of unknown size such as that produced by Non Dropouts Non The M.E. covers ONLY errors and does NOT compensate for. Conclusions drawn from statistical inference ( C.I. or Hyp. Test) are valid when the data is a from the population of interest. Our formulas for the M.E. are valid only for an. Beware of data collection our formulas do NOT compensate for sampling methods. Our formulas are when there are or the distribution is and the sample size is You MUST KNOW the standard deviation,. Eample From Gallup.com: "Negative assessments of the United States' involvement in Iraq continue to outweigh positive attitudes, but only by a slight margin. This finding is statistically similar to what Gallup found in June and July, but represents a slight improvement compared with early May % of Americans disapprove of the way President George W. Bush is handling Iraq,..." These results are based on telephone interviews with a randomly selected national sample of 1,017 adults, aged 18 and older, conducted Aug. 911, For results based on this sample, one can say with 95% confidence that the maimum error attributable to sampling and other random effects is ±3 percentage points. In addition to sampling error, question wording and practical difficulties in conducting surveys can introduce error or bias into the findings of public opinion polls. 5 Sta 245 Sec 6.1 SB
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 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 informationLesson 17: Margin of Error When Estimating a Population Proportion
Margin of Error When Estimating a Population Proportion Classwork In this lesson, you will find and interpret the standard deviation of a simulated distribution for a sample proportion and use this information
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 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 informationMargin of Error When Estimating a Population Proportion
Margin of Error When Estimating a Population Proportion Student Outcomes Students use data from a random sample to estimate a population proportion. Students calculate and interpret margin of error in
More information5.1 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 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 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 informationWhen σ Is Known: Recall the Mystery Mean Activity where x bar = 240.79 and we have an SRS of size 16
8.3 ESTIMATING A POPULATION MEAN When σ Is Known: Recall the Mystery Mean Activity where x bar = 240.79 and we have an SRS of size 16 Task was to estimate the mean when we know that the situation is Normal
More information5/31/2013. 6.1 Normal Distributions. Normal Distributions. Chapter 6. Distribution. The Normal Distribution. Outline. Objectives.
The Normal Distribution C H 6A P T E R The Normal Distribution Outline 6 1 6 2 Applications of the Normal Distribution 6 3 The Central Limit Theorem 6 4 The Normal Approximation to the Binomial Distribution
More informationChapter 1112 1 Review
Chapter 1112 Review Name 1. In formulating hypotheses for a statistical test of significance, the null hypothesis is often a statement of no effect or no difference. the probability of observing the data
More informationSection 63 DoubleAngle and HalfAngle Identities
63 DoubleAngle and HalfAngle Identities 47 Section 63 DoubleAngle and HalfAngle Identities DoubleAngle Identities HalfAngle Identities This section develops another important set of identities
More informationDef: The standard normal distribution is a normal probability distribution that has a mean of 0 and a standard deviation of 1.
Lecture 6: Chapter 6: Normal Probability Distributions A normal distribution is a continuous probability distribution for a random variable x. The graph of a normal distribution is called the normal curve.
More information= 2.0702 N(280, 2.0702)
Name Test 10 Confidence Intervals Homework (Chpt 10.1, 11.1, 12.1) Period For 1 & 2, determine the point estimator you would use and calculate its value. 1. How many pairs of shoes, on average, do female
More informationConfidence intervals
Confidence intervals Today, we re going to start talking about confidence intervals. We use confidence intervals as a tool in inferential statistics. What this means is that given some sample statistics,
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 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 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 informationSection 37. Marginal Analysis in Business and Economics. Marginal Cost, Revenue, and Profit. 202 Chapter 3 The Derivative
202 Chapter 3 The Derivative Section 37 Marginal Analysis in Business and Economics Marginal Cost, Revenue, and Profit Application Marginal Average Cost, Revenue, and Profit Marginal Cost, Revenue, and
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 informationChapter 7 Part 2. Hypothesis testing Power
Chapter 7 Part 2 Hypothesis testing Power November 6, 2008 All of the normal curves in this handout are sampling distributions Goal: To understand the process of hypothesis testing and the relationship
More informationAssociation Between Variables
Contents 11 Association Between Variables 767 11.1 Introduction............................ 767 11.1.1 Measure of Association................. 768 11.1.2 Chapter Summary.................... 769 11.2 Chi
More informationModule 5 Hypotheses Tests: Comparing Two Groups
Module 5 Hypotheses Tests: Comparing Two Groups Objective: In medical research, we often compare the outcomes between two groups of patients, namely exposed and unexposed groups. At the completion of this
More informationRandom variables, probability distributions, binomial random variable
Week 4 lecture notes. WEEK 4 page 1 Random variables, probability distributions, binomial random variable Eample 1 : Consider the eperiment of flipping a fair coin three times. The number of tails that
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 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 informationSurvey Sampling. Know How No 9 guidance for research and evaluation in Fife. What this is about? Who is it for? What do you need to know?
guidance for research and evaluation in Fife What this is about? Sampling allows you to draw conclusions about a particular population by examining a part of it. When carrying out a survey, it is not usually
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 informationMethods to Solve Quadratic Equations
Methods to Solve Quadratic Equations We have been learning how to factor epressions. Now we will apply factoring to another skill you must learn solving quadratic equations. a b c 0 is a seconddegree
More informationSolving Quadratic Equations by Graphing. Consider an equation of the form. y ax 2 bx c a 0. In an equation of the form
SECTION 11.3 Solving Quadratic Equations b Graphing 11.3 OBJECTIVES 1. Find an ais of smmetr 2. Find a verte 3. Graph a parabola 4. Solve quadratic equations b graphing 5. Solve an application involving
More informationChapter 1 Introduction to Econometrics
Chapter 1 Introduction to Econometrics Econometrics deals with the measurement of economic relationships. It is an integration of economics, mathematical economics and statistics with an objective to provide
More informationFigure 1.1 Percentage of persons without health insurance coverage: all ages, United States, 19972001
Figure 1.1 Percentage of persons without health insurance coverage: all ages, United States, 19972001 DATA SOURCE: Family Core component of the 19972001 National Health Interview Surveys. The estimate
More informationMBA 611 STATISTICS AND QUANTITATIVE METHODS
MBA 611 STATISTICS AND QUANTITATIVE METHODS Part I. Review of Basic Statistics (Chapters 111) A. Introduction (Chapter 1) Uncertainty: Decisions are often based on incomplete information from uncertain
More informationHypothesis. Testing Examples and Case Studies. Chapter 23. Copyright 2005 Brooks/Cole, a division of Thomson Learning, Inc.
Hypothesis Chapter 23 Testing Examples and Case Studies Copyright 2005 Brooks/Cole, a division of Thomson Learning, Inc. 23.1 How Hypothesis Tests Are Reported in the News 1. Determine the null hypothesis
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 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 214 (NOTES) Math 214 Al Nosedal. Department of Mathematics Indiana University of Pennsylvania. MATH 214 (NOTES) p. 1/6
MATH 214 (NOTES) Math 214 Al Nosedal Department of Mathematics Indiana University of Pennsylvania MATH 214 (NOTES) p. 1/6 "Pepsi" problem A market research consultant hired by the PepsiCola Co. is interested
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 informationMath 251, Review Questions for Test 3 Rough Answers
Math 251, Review Questions for Test 3 Rough Answers 1. (Review of some terminology from Section 7.1) In a state with 459,341 voters, a poll of 2300 voters finds that 45 percent support the Republican candidate,
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 informationSampling Distribution of a Normal Variable
Ismor Fischer, 5/9/01 5.1 5. Formal Statement and Examples Comments: Sampling Distribution of a Normal Variable Given a random variable. Suppose that the population distribution of is known to be normal,
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 informationResearch Design Concepts. Independent and dependent variables Data types Sampling Validity and reliability
Research Design Concepts Independent and dependent variables Data types Sampling Validity and reliability Research Design Action plan for carrying out research How the research will be conducted to investigate
More informationTImath.com. Statistics. Areas in Intervals
Areas in Intervals ID: 9472 TImath.com Time required 30 minutes Activity Overview In this activity, students use several methods to determine the probability of a given normally distributed value being
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 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 informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Sample Final Exam Spring 2008 DeMaio Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the given degree of confidence and sample data to construct
More informationResearch Variables. Measurement. Scales of Measurement. Chapter 4: Data & the Nature of Measurement
Chapter 4: Data & the Nature of Graziano, Raulin. Research Methods, a Process of Inquiry Presented by Dustin Adams Research Variables Variable Any characteristic that can take more than one form or value.
More informationChapter 7 Section 7.1: Inference for the Mean of a Population
Chapter 7 Section 7.1: Inference for the Mean of a Population Now let s look at a similar situation Take an SRS of size n Normal Population : N(, ). Both and are unknown parameters. Unlike what we used
More informationSampling and Hypothesis Testing
Population and sample Sampling and Hypothesis Testing Allin Cottrell Population : an entire set of objects or units of observation of one sort or another. Sample : subset of a population. Parameter versus
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 informationChapter 7 Notes  Inference for Single Samples. You know already for a large sample, you can invoke the CLT so:
Chapter 7 Notes  Inference for Single Samples You know already for a large sample, you can invoke the CLT so: X N(µ, ). Also for a large sample, you can replace an unknown σ by s. You know how to do a
More informationProbability Distributions
Learning Objectives Probability Distributions Section 1: How Can We Summarize Possible Outcomes and Their Probabilities? 1. Random variable 2. Probability distributions for discrete random variables 3.
More informationAP Statistics 2002 Scoring Guidelines
AP Statistics 2002 Scoring Guidelines The materials included in these files are intended for use by AP teachers for course and exam preparation in the classroom; permission for any other use must be sought
More informationChapter 4. Probability and Probability Distributions
Chapter 4. robability and robability Distributions Importance of Knowing robability To know whether a sample is not identical to the population from which it was selected, it is necessary to assess the
More informationSTATISTICS 8 CHAPTERS 1 TO 6, SAMPLE MULTIPLE CHOICE QUESTIONS
STATISTICS 8 CHAPTERS 1 TO 6, SAMPLE MULTIPLE CHOICE QUESTIONS Correct answers are in bold italics.. This scenario applies to Questions 1 and 2: A study was done to compare the lung capacity of coal miners
More informationSection 33 Approximating Real Zeros of Polynomials
 Approimating Real Zeros of Polynomials 9 Section  Approimating Real Zeros of Polynomials Locating Real Zeros The Bisection Method Approimating Multiple Zeros Application The methods for finding zeros
More informationDomain of a Composition
Domain of a Composition Definition Given the function f and g, the composition of f with g is a function defined as (f g)() f(g()). The domain of f g is the set of all real numbers in the domain of g such
More information1) What is the probability that the random variable has a value greater than 2? A) 0.750 B) 0.625 C) 0.875 D) 0.700
Practice for Chapter 6 & 7 Math 227 This is merely an aid to help you study. The actual exam is not multiple choice nor is it limited to these types of questions. Using the following uniform density curve,
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 informationObjectives. 6.1, 7.1 Estimating with confidence (CIS: Chapter 10) CI)
Objectives 6.1, 7.1 Estimating with confidence (CIS: Chapter 10) Statistical confidence (CIS gives a good explanation of a 95% CI) Confidence intervals. Further reading http://onlinestatbook.com/2/estimation/confidence.html
More information. 58 58 60 62 64 66 68 70 72 74 76 78 Father s height (inches)
PEARSON S FATHERSON DATA The following scatter diagram shows the heights of 1,0 fathers and their fullgrown sons, in England, circa 1900 There is one dot for each fatherson pair Heights of fathers and
More informationConstruct a scatterplot for the given data. 2) x Answer:
Review for Test 5 STA 2023 spr 2014 Name Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents
More informationExtending Hypothesis Testing. pvalues & confidence intervals
Extending Hypothesis Testing pvalues & confidence intervals So far: how to state a question in the form of two hypotheses (null and alternative), how to assess the data, how to answer the question by
More informationHigher. Polynomials and Quadratics 64
hsn.uk.net Higher Mathematics UNIT OUTCOME 1 Polnomials and Quadratics Contents Polnomials and Quadratics 64 1 Quadratics 64 The Discriminant 66 3 Completing the Square 67 4 Sketching Parabolas 70 5 Determining
More informationFACTORING ax 2 bx c WITH a 1
296 (6 20) Chapter 6 Factoring 6.4 FACTORING a 2 b c WITH a 1 In this section The ac Method Trial and Error Factoring Completely In Section 6.3 we factored trinomials with a leading coefficient of 1. In
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 information10.1. Solving Quadratic Equations. Investigation: Rocket Science CONDENSED
CONDENSED L E S S O N 10.1 Solving Quadratic Equations In this lesson you will look at quadratic functions that model projectile motion use tables and graphs to approimate solutions to quadratic equations
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 informationTwosample inference: Continuous data
Twosample inference: Continuous data Patrick Breheny April 5 Patrick Breheny STA 580: Biostatistics I 1/32 Introduction Our next two lectures will deal with twosample inference for continuous data As
More informationSample Exam #1 Elementary Statistics
Sample Exam #1 Elementary Statistics Instructions. No books, notes, or calculators are allowed. 1. Some variables that were recorded while studying diets of sharks are given below. Which of the variables
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 informationHomework 5 Solutions
Math 130 Assignment Chapter 18: 6, 10, 38 Chapter 19: 4, 6, 8, 10, 14, 16, 40 Chapter 20: 2, 4, 9 Chapter 18 Homework 5 Solutions 18.6] M&M s. The candy company claims that 10% of the M&M s it produces
More informationCarolyn Anderson & Youngshil Paek (Slides created by Shuai Sam Wang) Department of Educational Psychology University of Illinois at UrbanaChampaign
Carolyn Anderson & Youngshil Paek (Slides created by Shuai Sam Wang) Department of Educational Psychology University of Illinois at UrbanaChampaign Key Points 1. Data 2. Variable 3. Types of data 4. Define
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 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 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 informationNonparametric tests, Bootstrapping
Nonparametric tests, Bootstrapping http://www.isrec.isbsib.ch/~darlene/embnet/ Hypothesis testing review 2 competing theories regarding a population parameter: NULL hypothesis H ( straw man ) ALTERNATIVEhypothesis
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 informationChapter 7 Review. Confidence Intervals. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Chapter 7 Review Confidence Intervals MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Suppose that you wish to obtain a confidence interval for
More information6 3 The Standard Normal Distribution
290 Chapter 6 The Normal Distribution Figure 6 5 Areas Under a Normal Distribution Curve 34.13% 34.13% 2.28% 13.59% 13.59% 2.28% 3 2 1 + 1 + 2 + 3 About 68% About 95% About 99.7% 6 3 The Distribution Since
More informationBinomial Random Variables
Binomial Random Variables Dr Tom Ilvento Department of Food and Resource Economics Overview A special case of a Discrete Random Variable is the Binomial This happens when the result of the eperiment is
More informationImputation and Analysis. Peter Fayers
Missing Data in Palliative Care Research Imputation and Analysis Peter Fayers Department of Public Health University of Aberdeen NTNU Det medisinske fakultet Missing data Missing data is a major problem
More informationContents. 6 Graph Sketching 87. 6.1 Increasing Functions and Decreasing Functions... 87. 6.2 Intervals Monotonically Increasing or Decreasing...
Contents 6 Graph Sketching 87 6.1 Increasing Functions and Decreasing Functions.......................... 87 6.2 Intervals Monotonically Increasing or Decreasing....................... 88 6.3 Etrema Maima
More informationHypothesis Testing and Confidence Interval Estimation
Biostatistics for Health Care Researchers: A Short Course Hypothesis Testing and Confidence Interval Estimation Presented ed by: Susan M. Perkins, Ph.D. Division of Biostatistics Indiana University School
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 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 informationStatewide Survey of Louisiana Likely Voters on David Duke
Statewide Survey of Louisiana Likely Voters on David Duke The University of New Orleans Survey Research Center (SRC) sponsored an automated interactive voice response (IVR) telephone survey of likely Louisiana
More informationExponential Functions. Exponential Functions and Their Graphs. Example 2. Example 1. Example 3. Graphs of Exponential Functions 9/17/2014
Eponential Functions Eponential Functions and Their Graphs Precalculus.1 Eample 1 Use a calculator to evaluate each function at the indicated value of. a) f ( ) 8 = Eample In the same coordinate place,
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 information3.5 Summary of Curve Sketching
3.5 Summary of Curve Sketching Follow these steps to sketch the curve. 1. Domain of f() 2. and y intercepts (a) intercepts occur when f() = 0 (b) yintercept occurs when = 0 3. Symmetry: Is it even or
More informationWashington Post ABC News Poll Iraq: June 2005
Washington Post ABC News Poll Iraq: June 2005 This Washington PostABC News poll was conducted by telephone June 2326, 2005 among 1,004 randomly selected adults nationwide. Margin of sampling error for
More informationBasic Probability Theory I
A Probability puzzler!! Basic Probability Theory I Dr. Tom Ilvento FREC 408 Our Strategy with Probability Generally, we want to get to an inference from a sample to a population. In this case the population
More informationNATIONAL: SENATE SHOULD CONSIDER SCOTUS PICK
Please attribute this information to: Monmouth University Poll West Long Branch, NJ 07764 www.monmouth.edu/polling Follow on Twitter: @MonmouthPoll Released: Monday, March 21, 2016 Contact: PATRICK MURRAY
More informationThe Margin of Error for Differences in Polls
The Margin of Error for Differences in Polls Charles H. Franklin University of Wisconsin, Madison October 27, 2002 (Revised, February 9, 2007) The margin of error for a poll is routinely reported. 1 But
More informationMath 108 Exam 3 Solutions Spring 00
Math 108 Exam 3 Solutions Spring 00 1. An ecologist studying acid rain takes measurements of the ph in 12 randomly selected Adirondack lakes. The results are as follows: 3.0 6.5 5.0 4.2 5.5 4.7 3.4 6.8
More informationMarist College Institute for Public Opinion Poughkeepsie, NY 12601 Phone 845.575.5050 Fax 845.575.5111
Marist College Institute for Public Opinion Poughkeepsie, NY 12601 Phone 845.575.5050 Fax 845.575.5111 www.maristpoll.marist.edu POLL MUST BE SOURCED: NBC News/Marist Poll* Louisiana: Landrieu Leads Cassidy
More informationComparing Two Groups. Standard Error of ȳ 1 ȳ 2. Setting. Two Independent Samples
Comparing Two Groups Chapter 7 describes two ways to compare two populations on the basis of independent samples: a confidence interval for the difference in population means and a hypothesis test. The
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 information