P(every one of the seven intervals covers the true mean yield at its location) = 3.


 Bernard Dean
 2 years ago
 Views:
Transcription
1 1 Let = number of locations at which the computed confidence interval for that location hits the true value of the mean yield at its location has a binomial(7,095) (a) P(every one of the seven intervals covers the true mean yield at its location) = 3 The overall confidence level for the seven simultaneous statements is only 689% (b) 2 (a) (b) 3 Let Now, if and only if (a) Let has a under the alternative value (b) Let has a under the alternative value
2 (c) The power to detect the alternative mean value 295 is greater than for the alternative mean value 299 since it is easier to detect a value of µ which is further away from the null mean value (a) The boxplot suggests that the distribution of the data values is fairly symmetric No outliers are identified by the plot The value 110 litres/minute for the mean maximum voluntary ventilation value considered in part (c) is close to the center of the distribution of the data values as measured by the median (b) Let µ be the mean maximum voluntary ventilation value for this population of healthy college seniors 1116 litres/minute litres/minute litres/minute
3 For 95% confidence, A 95% confidence interval for µ is given by We are 95% confident that the mean maximum voluntary ventilation value for this population of healthy college seniors is between 8525 litres/minute and litres/minute (c) litres/minute litres/minute Since the value 110 is inside the 95% confidence interval in (b), these data are not statistically significant at the 5% level At the 5% level, one would accept At the 5% level, these data are consistent with the mean maximum voluntary ventilation value being 110 litres/minute (d) The analysis assumes the observations are independent and normally distributed Since our sample is a simple random sample, the observations are independent if the population size is much larger than the sample size Since there are no outliers and, even if the distribution of the maximum voluntary ventilation values is even somewhat skewed in the population, and hence not normally distributed, our confidence level will still be reasonably accurate In fact, the normal quantilequantile plot (or equivalently, normal probability plot) does not suggest that there is a significant problem with the normal assumption that would affect the analysis It could easily arise even with independent and normally distributed data with
4 5 Let µ be the mean diameter (in mm) of a skin test reaction for the population of adolescents who might participate in an immunologic study of this kind mm mm mm (a) mm mm Since we reject in favour of at the 1% level These data provide evidence at the 1% level that the mean diameter of the skin test reaction to the antigen is less than 30 mm (b) for 98% confidence mm A 98% confidence interval for µ is given by: We are 98% confident that the mean diameter of the skin test reaction for this population of adolescents is between 17 mm and 25 mm (c) The key assumption here for the analysis to be valid is that the diameters from different subjects be independent If different subjects respond independently to the skin test, this would be the case Since, the normal assumption is not necessary and the stated confidence level and significance levels will be reasonably accurate even if the distribution of diameter of the skin test reaction is strongly skewed in the population
5 6 It was expected that the blood stream concentration of a particular antibiotic one hour after its administration could vary substantially from individual to individual The study was therefore designed as a matched pairs study where the same individual was exposed to both antibiotics This allows a comparison between the two antibiotics while holding subject constant Person Penicillin Amoxicillin Difference (d=penamox) Let be the mean difference in blood stream concentration between penicillin and amoxicillin one hour after administration g/ml g/ml g/ml (a) Large values of provide evidence against in the direction of Using table C3, These data are consistent with the mean blood stream concentrations one hour after administration being the same for the two antibiotics In particular, these data are not even statistically significant at the 20% level (b) for 95% confidence A 95% confidence interval for is given by:
6 With 95% confidence, the mean blood stream concentration one hour after administration of pencillicin could be as much as 874 µg/ml less than amoxicillin or as much as 474 µg/ml more than amoxicillin according to our data (c) We assume that the differences are independent This will be the case if the subjects respond independently Independence of the two responses within subject is not necessary for this analysis We also assume that the differences are normally distributed It is important that this be based on past experience since these data alone possess very little information regarding this issue Moreover, since is very small, we cannot rely on the robustness properties of the onesample procedures associated with larger sample sizes The normal quantilequantile plot (or equivalently, normal probability plot) does not indicate a departure from normality 7 Let the mean protoporphyrin level for the population of adult male alcoholics with ring sideroblasts in the bone marrow that were sampled Let the standard deviation of the protoporphyrin level for the population of adult male alcoholics with ring sideroblasts in the bone marrow Let the mean protoporphyrin level for the population of apparently healthy nonalchoholic adult males that were sampled Let the standard deviation of the protoporphyrin level for the population of apparently healthy nonalchoholic adult males that were sampled
7 The ratio of the largest sample variance to the smallest sample variance which is much greater than a typical cutoff value of 3 (or the more conservative cutoff value 2) often used in practice to rule out the safe application of pooled procedures that assume equal population standard deviations when sample sizes are not nearly equal as is the case here If the protoporphyrin level in each population is normally distributed (not indicated here!), the two critical values for a test of : against : with are and Since we would as expected reject This test is neither necessary nor recommended in this situation It is highly nonrobust to departures from normality (a) Satterthwaite s degrees of freedom are: Large values of provide evidence against in the direction of Using Table C3, These data provide extremely strong evidence that the mean protoporphyrin level is higher in the represented alcoholic population than in the nonalcoholic population In particular, these data are statistically significant at the 05% level (b) To get the critical value for 99% confidence using table C3 we can round down to 50
8 The 99% confidence interval for is given by: 390) With 99% confidence, the mean protoporphyrin level is between 200 and 390 units greater in the represented alcoholic population than in the nonalcoholic population Using a computer, the value of without rounding is which yields the same interval in this case 8 (a) This is a completely randomized design (b) The distribution of the data values for the sensory deprivation treatment group is shifted towards lower values and has greater spread than that of the control group In particular, at least 75% of the data values in the control group are above the third quartile of the sensory deprivation treatment group There is a single outlier that was identified for the control group
9 (c) Let the mean alphawave frequency for a randomly selected individual when exposed to the sensory deprivation treatment Let the mean alphawave frequency for a randomly selected individual when treated as a control subject = Large values of provide evidence against in the direction of Using table C3, Hence, these data provide very strong evidence that the mean alphawave frequency under the deprived sensory treatment is different from that of the control treatment In particular, these data are statistically significant at the 05% level (d) for 95% confidence The 95% confidence interval for is given by:
10 We are 95% confident that the mean alphawave frequency under the deprived sensory treatment is between 030 and 130 units lower than under the control treatment (e) It seems reasonable to expect that the two samples are independent Provided exposure to a treatment for a subject occurred independently of other subjects subjected to the same treatment, responses within a specific treatment should also be independent The normal quantilequantile (or equivalently normal probability plot) for the deprived sensory treatment group does not indicate a departure from normality There is a value in the control group that is somewhat outlying With any outlier it is important to consider its potential cause Is it a recording error or an experimental error? Is it indicative of a different mechanism that is at play? How one proceeds depends on the reason for an outlier Here, it is probably chance variation associated with the underlying distribution among subjects subjected to the control treatment Even if this is not exactly normal for this group, since the sample sizes are equal, and moreover,, we can expect our pooled procedures to be quite robust to departures from equal variances, and moreover, normality in the absence of strong skewness Our plots do not indicate departures from the assumptions that would affect the validity of the analysis Normal quantilequantile plot for the sensory deprivation group:
11 Normal quantilequantile plot for the control group:
General Method: Difference of Means. 3. Calculate df: either WelchSatterthwaite formula or simpler df = min(n 1, n 2 ) 1.
General Method: Difference of Means 1. Calculate x 1, x 2, SE 1, SE 2. 2. Combined SE = SE1 2 + SE2 2. ASSUMES INDEPENDENT SAMPLES. 3. Calculate df: either WelchSatterthwaite formula or simpler df = min(n
More informationF. Farrokhyar, MPhil, PhD, PDoc
Learning objectives Descriptive Statistics F. Farrokhyar, MPhil, PhD, PDoc To recognize different types of variables To learn how to appropriately explore your data How to display data using graphs How
More informationUnit 27: Comparing Two Means
Unit 27: Comparing Two Means Prerequisites Students should have experience with onesample tprocedures before they begin this unit. That material is covered in Unit 26, Small Sample Inference for One
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 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 informationOutline of Topics. Statistical Methods I. Types of Data. Descriptive Statistics
Statistical Methods I Tamekia L. Jones, Ph.D. (tjones@cog.ufl.edu) Research Assistant Professor Children s Oncology Group Statistics & Data Center Department of Biostatistics Colleges of Medicine and Public
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 informationAn example ANOVA situation. 1Way ANOVA. Some notation for ANOVA. Are these differences significant? Example (Treating Blisters)
An example ANOVA situation Example (Treating Blisters) 1Way ANOVA MATH 143 Department of Mathematics and Statistics Calvin College Subjects: 25 patients with blisters Treatments: Treatment A, Treatment
More informationCHAPTER 14 NONPARAMETRIC TESTS
CHAPTER 14 NONPARAMETRIC TESTS Everything that we have done up until now in statistics has relied heavily on one major fact: that our data is normally distributed. We have been able to make inferences
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 information, then the form of the model is given by: which comprises a deterministic component involving the three regression coefficients (
Multiple regression Introduction Multiple regression is a logical extension of the principles of simple linear regression to situations in which there are several predictor variables. For instance if we
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 informationExploratory data analysis (Chapter 2) Fall 2011
Exploratory data analysis (Chapter 2) Fall 2011 Data Examples Example 1: Survey Data 1 Data collected from a Stat 371 class in Fall 2005 2 They answered questions about their: gender, major, year in school,
More informationStatistics I for QBIC. Contents and Objectives. Chapters 1 7. Revised: August 2013
Statistics I for QBIC Text Book: Biostatistics, 10 th edition, by Daniel & Cross Contents and Objectives Chapters 1 7 Revised: August 2013 Chapter 1: Nature of Statistics (sections 1.11.6) Objectives
More informationPaired vs. 2 sample comparisons. Comparing means. Paired comparisons allow us to account for a lot of extraneous variation.
Comparing means! Tests with one categorical and one numerical variable Paired vs. sample comparisons! Goal: to compare the mean of a numerical variable for different groups. Paired comparisons allow us
More informationAnalysis of numerical data S4
Basic medical statistics for clinical and experimental research Analysis of numerical data S4 Katarzyna Jóźwiak k.jozwiak@nki.nl 3rd November 2015 1/42 Hypothesis tests: numerical and ordinal data 1 group:
More informationVersions 1a Page 1 of 17
Note to Students: This practice exam is intended to give you an idea of the type of questions the instructor asks and the approximate length of the exam. It does NOT indicate the exact questions or 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 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 informationIntroduction to Statistics for Computer Science Projects
Introduction Introduction to Statistics for Computer Science Projects Peter Coxhead Whole modules are devoted to statistics and related topics in many degree programmes, so in this short session all I
More informationMTH 140 Statistics Videos
MTH 140 Statistics Videos Chapter 1 Picturing Distributions with Graphs Individuals and Variables Categorical Variables: Pie Charts and Bar Graphs Categorical Variables: Pie Charts and Bar Graphs Quantitative
More informationWording of Final Conclusion. Slide 1
Wording of Final Conclusion Slide 1 8.3: Assumptions for Testing Slide 2 Claims About Population Means 1) The sample is a simple random sample. 2) The value of the population standard deviation σ is known
More information9.1 (a) The standard deviation of the four sample differences is given as.68. The standard error is SE (ȳ1  ȳ 2 ) = SE d  = s d n d
CHAPTER 9 Comparison of Paired Samples 9.1 (a) The standard deviation of the four sample differences is given as.68. The standard error is SE (ȳ1  ȳ 2 ) = SE d  = s d n d =.68 4 =.34. (b) H 0 : The mean
More informationLecture 2: Descriptive Statistics and Exploratory Data Analysis
Lecture 2: Descriptive Statistics and Exploratory Data Analysis Further Thoughts on Experimental Design 16 Individuals (8 each from two populations) with replicates Pop 1 Pop 2 Randomly sample 4 individuals
More informationUNDERSTANDING THE INDEPENDENTSAMPLES t TEST
UNDERSTANDING The independentsamples t test evaluates the difference between the means of two independent or unrelated groups. That is, we evaluate whether the means for two independent groups are significantly
More informationBASIC STATISTICAL METHODS FOR GENOMIC DATA ANALYSIS
BASIC STATISTICAL METHODS FOR GENOMIC DATA ANALYSIS SEEMA JAGGI Indian Agricultural Statistics Research Institute Library Avenue, New Delhi110 012 seema@iasri.res.in Genomics A genome is an organism s
More informationStatistiek I. ttests. John Nerbonne. CLCG, Rijksuniversiteit Groningen. John Nerbonne 1/35
Statistiek I ttests John Nerbonne CLCG, Rijksuniversiteit Groningen http://wwwletrugnl/nerbonne/teach/statistieki/ John Nerbonne 1/35 ttests To test an average or pair of averages when σ is known, we
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 informationChapter 7 Section 1 Homework Set A
Chapter 7 Section 1 Homework Set A 7.15 Finding the critical value t *. What critical value t * from Table D (use software, go to the web and type t distribution applet) should be used to calculate the
More informationa) Find the five point summary for the home runs of the National League teams. b) What is the mean number of home runs by the American League teams?
1. Phone surveys are sometimes used to rate TV shows. Such a survey records several variables listed below. Which ones of them are categorical and which are quantitative?  the number of people watching
More informationHypothesis Testing ExercisesPrintable Page 1 of 7
Hypothesis Testing ExercisesPrintable Page 1 of 7 BioEpi 540 Home > Topics > Hypothesis Testing > Exercises Topics Hypothesis Testing Exercises (to print: pdf 35k 7 pages) HT1. [Solution pdf 101k 4 pages
More informationDescriptive Statistics. Understanding Data: Categorical Variables. Descriptive Statistics. Dataset: Shellfish Contamination
Descriptive Statistics Understanding Data: Dataset: Shellfish Contamination Location Year Species Species2 Method Metals Cadmium (mg kg  ) Chromium (mg kg  ) Copper (mg kg  ) Lead (mg kg  ) Mercury
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 informationParametric and nonparametric statistical methods for the life sciences  Session I
Why nonparametric methods What test to use? Rank Tests Parametric and nonparametric statistical methods for the life sciences  Session I Liesbeth Bruckers Geert Molenberghs Interuniversity Institute
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 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 informationUnit 24 Hypothesis Tests about Means
Unit 24 Hypothesis Tests about Means Objectives: To recognize the difference between a paired t test and a twosample t test To perform a paired t test To perform a twosample t test A measure of the amount
More informationStatistics and research
Statistics and research Usaneya Perngparn Chitlada Areesantichai Drug Dependence Research Center (WHOCC for Research and Training in Drug Dependence) College of Public Health Sciences Chulolongkorn University,
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 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 informationSeminar paper Statistics
Seminar paper Statistics The seminar paper must contain:  the title page  the characterization of the data (origin, reason why you have chosen this analysis,...)  the list of the data (in the table)
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 informationStatistics 641  EXAM II  1999 through 2003
Statistics 641  EXAM II  1999 through 2003 December 1, 1999 I. (40 points ) Place the letter of the best answer in the blank to the left of each question. (1) In testing H 0 : µ 5 vs H 1 : µ > 5, the
More informationAP Statistics 2001 Solutions and Scoring Guidelines
AP Statistics 2001 Solutions and Scoring Guidelines The materials included in these files are intended for noncommercial use by AP teachers for course and exam preparation; permission for any other use
More information12: Analysis of Variance. Introduction
1: Analysis of Variance Introduction EDA Hypothesis Test Introduction In Chapter 8 and again in Chapter 11 we compared means from two independent groups. In this chapter we extend the procedure to consider
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 informationStatistics 101 Homework 2
Statistics 101 Homework 2 Solution Reading: January 23 January 25 Chapter 4 January 28 Chapter 5 Assignment: 1. As part of a physiology study participants had their heart rate (beats per minute) taken
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 informationAP Statistics 2005 Scoring Guidelines
AP Statistics 2005 Scoring Guidelines The College Board: Connecting Students to College Success The College Board is a notforprofit membership association whose mission is to connect students to college
More information= $96 = $24. (b) The degrees of freedom are. s n. 7.3. For the mean monthly rent, the 95% confidence interval for µ is
Chapter 7 Solutions 71 (a) The standard error of the mean is df = n 1 = 15 s n = $96 = $24 (b) The degrees of freedom are 16 72 In each case, use df = n 1; if that number is not in Table D, drop to the
More information1. 2. 3. 4. Find the mean and median. 5. 1, 2, 87 6. 3, 2, 1, 10. Bellwork 32315 Simplify each expression.
Bellwork 32315 Simplify each expression. 1. 2. 3. 4. Find the mean and median. 5. 1, 2, 87 6. 3, 2, 1, 10 1 Objectives Find measures of central tendency and measures of variation for statistical data.
More informationNumerical Summarization of Data OPRE 6301
Numerical Summarization of Data OPRE 6301 Motivation... In the previous session, we used graphical techniques to describe data. For example: While this histogram provides useful insight, other interesting
More information1 Confidence intervals
Math 143 Inference for Means 1 Statistical inference is inferring information about the distribution of a population from information about a sample. We re generally talking about one of two things: 1.
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 informationCenter: Finding the Median. Median. Spread: Home on the Range. Center: Finding the Median (cont.)
Center: Finding the Median When we think of a typical value, we usually look for the center of the distribution. For a unimodal, symmetric distribution, it s easy to find the center it s just the center
More informationProbability and Statistics Lecture 9: 1 and 2Sample Estimation
Probability and Statistics Lecture 9: 1 and Sample Estimation to accompany Probability and Statistics for Engineers and Scientists Fatih Cavdur Introduction A statistic θ is said to be an unbiased estimator
More informationDr. Peter Tröger Hasso Plattner Institute, University of Potsdam. Software Profiling Seminar, Statistics 101
Dr. Peter Tröger Hasso Plattner Institute, University of Potsdam Software Profiling Seminar, 2013 Statistics 101 Descriptive Statistics Population Object Object Object Sample numerical description Object
More informationWe will use the following data sets to illustrate measures of center. DATA SET 1 The following are test scores from a class of 20 students:
MODE The mode of the sample is the value of the variable having the greatest frequency. Example: Obtain the mode for Data Set 1 77 For a grouped frequency distribution, the modal class is the class having
More informationNonparametric TwoSample Tests. Nonparametric Tests. Sign Test
Nonparametric TwoSample Tests Sign test MannWhitney Utest (a.k.a. Wilcoxon twosample test) KolmogorovSmirnov Test Wilcoxon SignedRank Test TukeyDuckworth Test 1 Nonparametric Tests Recall, nonparametric
More informationTesting: is my coin fair?
Testing: is my coin fair? Formally: we want to make some inference about P(head) Try it: toss coin several times (say 7 times) Assume that it is fair ( P(head)= ), and see if this assumption is compatible
More informationChapter Five: Paired Samples Methods 1/38
Chapter Five: Paired Samples Methods 1/38 5.1 Introduction 2/38 Introduction Paired data arise with some frequency in a variety of research contexts. Patients might have a particular type of laser surgery
More informationHow Far is too Far? Statistical Outlier Detection
How Far is too Far? Statistical Outlier Detection Steven Walfish President, Statistical Outsourcing Services steven@statisticaloutsourcingservices.com 30325329 Outline What is an Outlier, and Why are
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 informationMEASURES OF LOCATION AND SPREAD
Paper TU04 An Overview of Nonparametric Tests in SAS : When, Why, and How Paul A. Pappas and Venita DePuy Durham, North Carolina, USA ABSTRACT Most commonly used statistical procedures are based on the
More informationExploratory Data Analysis
Exploratory Data Analysis Johannes Schauer johannes.schauer@tugraz.at Institute of Statistics Graz University of Technology Steyrergasse 17/IV, 8010 Graz www.statistics.tugraz.at February 12, 2008 Introduction
More informationSpearman s correlation
Spearman s correlation Introduction Before learning about Spearman s correllation it is important to understand Pearson s correlation which is a statistical measure of the strength of a linear relationship
More informationModule 4: Data Exploration
Module 4: Data Exploration Now that you have your data downloaded from the Streams Project database, the detective work can begin! Before computing any advanced statistics, we will first use descriptive
More informationComparing Two Populations OPRE 6301
Comparing Two Populations OPRE 6301 Introduction... In many applications, we are interested in hypotheses concerning differences between the means of two populations. For example, we may wish to decide
More informationThe calculations lead to the following values: d 2 = 46, n = 8, s d 2 = 4, s d = 2, SEof d = s d n s d n
EXAMPLE 1: Paired ttest and tinterval DBP Readings by Two Devices The diastolic blood pressures (DBP) of 8 patients were determined using two techniques: the standard method used by medical personnel
More informationSIMULATION STUDIES IN STATISTICS WHAT IS A SIMULATION STUDY, AND WHY DO ONE? What is a (Monte Carlo) simulation study, and why do one?
SIMULATION STUDIES IN STATISTICS WHAT IS A SIMULATION STUDY, AND WHY DO ONE? What is a (Monte Carlo) simulation study, and why do one? Simulations for properties of estimators Simulations for properties
More informationList of Examples. Examples 319
Examples 319 List of Examples DiMaggio and Mantle. 6 Weed seeds. 6, 23, 37, 38 Vole reproduction. 7, 24, 37 Wooly bear caterpillar cocoons. 7 Homophone confusion and Alzheimer s disease. 8 Gear tooth strength.
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Open book and note Calculator OK Multiple Choice 1 point each MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the mean for the given sample data.
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 informationDensity Curve. A density curve is the graph of a continuous probability distribution. It must satisfy the following properties:
Density Curve A density curve is the graph of a continuous probability distribution. It must satisfy the following properties: 1. The total area under the curve must equal 1. 2. Every point on the curve
More informationHow to choose a statistical test. Francisco J. Candido dos Reis DGOFMRP University of São Paulo
How to choose a statistical test Francisco J. Candido dos Reis DGOFMRP University of São Paulo Choosing the right test One of the most common queries in stats support is Which analysis should I use There
More informationPearson s correlation
Pearson s correlation Introduction Often several quantitative variables are measured on each member of a sample. If we consider a pair of such variables, it is frequently of interest to establish if there
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 informationSociology 6Z03 Topic 15: Statistical Inference for Means
Sociology 6Z03 Topic 15: Statistical Inference for Means John Fox McMaster University Fall 2016 John Fox (McMaster University) Soc 6Z03: Statistical Inference for Means Fall 2016 1 / 41 Outline: Statistical
More informationPractice Set 8b ST Spring 2014
Practice Set 8b ST 20  Spring 204 The following problem set will help you work with hypothesis testing.. Ex 8.7 (p. 400. Add the following parts: (c Explain why the assumption that interpupillary distance
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 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 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 informationACTM State ExamStatistics
ACTM State ExamStatistics For the 25 multiplechoice questions, make your answer choice and record it on the answer sheet provided. Once you have completed that section of the test, proceed to the tiebreaker
More informationHypothesis Testing. Dr. Bob Gee Dean Scott Bonney Professor William G. Journigan American Meridian University
Hypothesis Testing Dr. Bob Gee Dean Scott Bonney Professor William G. Journigan American Meridian University 1 AMU / BonTech, LLC, JourniTech Corporation Copyright 2015 Learning Objectives Upon successful
More informationCollege of the Canyons A. Morrow Math 140 Exam 3
College of the Canyons Name: A. Morrow Math 140 Exam 3 Answer the following questions NEATLY. Show all necessary work directly on the exam. Scratch paper will be discarded unread. 1 point each part unless
More informationSuppose we want to compare the average effectiveness of two treatments in a completely randomized experiment. In this case, the parameters µ 1
AP Statistics: 10.2: Comparing Two Means Name: Suppose we want to compare the average effectiveness of two treatments in a completely randomized experiment. In this case, the parameters µ 1 and µ 2 are
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 informationChapter 3 Descriptive Statistics: Numerical Measures. Learning objectives
Chapter 3 Descriptive Statistics: Numerical Measures Slide 1 Learning objectives 1. Single variable Part I (Basic) 1.1. How to calculate and use the measures of location 1.. How to calculate and use the
More informationData Analysis. Lecture Empirical Model Building and Methods (Empirische Modellbildung und Methoden) SS Analysis of Experiments  Introduction
Data Analysis Lecture Empirical Model Building and Methods (Empirische Modellbildung und Methoden) Prof. Dr. Dr. h.c. Dieter Rombach Dr. Andreas Jedlitschka SS 2014 Analysis of Experiments  Introduction
More informationStatistical Inference and ttests
1 Statistical Inference and ttests Objectives Evaluate the difference between a sample mean and a target value using a onesample ttest. Evaluate the difference between a sample mean and a target value
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 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 information1 SAMPLE SIGN TEST. NonParametric Univariate Tests: 1 Sample Sign Test 1. A nonparametric equivalent of the 1 SAMPLE TTEST.
NonParametric Univariate Tests: 1 Sample Sign Test 1 1 SAMPLE SIGN TEST A nonparametric equivalent of the 1 SAMPLE TTEST. ASSUMPTIONS: Data is nonnormally distributed, even after log transforming.
More informationTest 12 Tests of Significance Homework Part 1 (Chpts & 11.2)
Name Period Test 12 Tests of Significance Homework Part 1 (Chpts. 12.2 & 11.2) 1. School officials are interested in implementing a policy that would allow students to bring their own technology to school
More informationTwosample hypothesis testing, II 9.07 3/16/2004
Twosample hypothesis testing, II 9.07 3/16/004 Small sample tests for the difference between two independent means For twosample tests of the difference in mean, things get a little confusing, here,
More informationHypothesis testing: Examples. AMS7, Spring 2012
Hypothesis testing: Examples AMS7, Spring 2012 Example 1: Testing a Claim about a Proportion Sect. 7.3, # 2: Survey of Drinking: In a Gallup survey, 1087 randomly selected adults were asked whether they
More informationAnnouncements. Unit 4: Inference for numerical variables Lecture 1: Bootstrap, paired, and two sample. Rent in Durham.
Announcements Announcements Unit 4: Inference for numerical variables Lecture 1: Bootstrap, paired, and two sample Statistics 101 Mine ÇetinkayaRundel February 26, 2013 Extra credit due Thursday at the
More informationBasic Biostatistics for Clinical Research. Ramses F Sadek, PhD GRU Cancer Center
Basic Biostatistics for Clinical Research Ramses F Sadek, PhD GRU Cancer Center 1 1. Basic Concepts 2. Data & Their Presentation Part One 2 1. Basic Concepts Statistics Biostatistics Populations and samples
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 informationVariables. Exploratory Data Analysis
Exploratory Data Analysis Exploratory Data Analysis involves both graphical displays of data and numerical summaries of data. A common situation is for a data set to be represented as a matrix. There is
More information