Chapter 7 Section 1 Homework Set A


 Rodney Stevenson
 3 years ago
 Views:
Transcription
1 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 margin of error for a confidence interval for the mean of the population in each of the following situations? (a) A 95% confidence interval based on n = 15 observations. Using Excel I type =tinv(0.05, 14) and I get, 2.145, try it! Using applet at I enter the value which one of the tails, the left (area left of) and I hit compute! And bingo, you get the picture on the right. (b) A 95% confidence interval from an SRS of 25 observations. (c) A 90% confidence interval from a sample of size 25. On Excel I type =tinv(0.1, 24) and I get t * = Using the applet I mentioned in part (a) (d) These cases illustrate how the size of the margin of error depends upon the confidence level and the sample size. Summarize these relationships. As the sample size increases the value of t * decreases getting closer to the value of Z *
2 7.16 Distribution of the t statistic. Assume a sample size of n = 20. Draw a picture of the distribution of the t statistic under the null hypothesis. Use Table D (use software, like CrunchIt!! as well) and your picture to illustrate the values of the test statistic that would lead to rejection of the null hypothesis at the 5% level for a two sided alternative. I did this using applet at applet at program. setting the degrees of freedom to 19, and the Paint 7.19 More on one sided versus two sided P values. Suppose that x = 15.3 in the selling of the previous exercise. Would this change your P value? Use a sketch of the distribution of the test statistic under the null hypothesis to illustrate and explain your answer. This is problem Computer software reports x = 15.3 and P = 0.04 for a test of Ho: µ = 0 versus Ha: µ 0. Based on prior knowledge, you can justify testing the alternative Ha: µ > 0. What is the P value for your significance test? P( x < 15.3) = 0.02, thus the pvalue is 2(0.02) = If x = 15.3 then all that would change would be the direction of the effect. The p value in a two sided scenario would be the same; If we went to one sided where Ha: µ > 0, then the p value would be calculated by P( x > 15.3) = 0.98.
3 7.20 A one sample t test. The one sample t statistic for testing H 0 : µ = 10 H a : µ >10 from a sample of n =20 observations has the value t = (a) What are the degrees of freedom for this statistic? Degrees of freedom is 19. (b) Give the two critical values t* from Table D that bracket t. At 19 d.f < 2.10 < (c) Between what two values does the P value of the test fall? At 19 d.f < P(T > 2.10) < (d) Is the value t =2.10 significant at the 5% level? Is it significant at the 1% level? At the 5% significance t > 2.10 is statistically significant, since p value < < 0.05, but it is not statistically significant at 1%, since the p value > (e) If you have software available, find the exact P value Another onesample t test. The onesample t statistic for testing H 0 : µ = 60 H a : µ 60 from a sample of n = 24 observations has the value t = (a) What are the degrees of freedom for t? (b) Locate the two critical values t* from Table D that bracket t. (c) Between what two values does the Pvalue of the test fall (From Table D)? (d) Is the value t = 2.40 statistically significant at the 5% level? At the 1% level?
4 (e) If you have software available, find the exact Pvalue 7.25 Random distribution of trees t test. A study of 584 longleaf pine trees in the Wade Tract in Thomas County, Georgia, is described in Example 6.1 (page 354). For each tree in the tract, the researchers measured the diameter at breast height (DBH). This is the diameter of the tree at 4.5 feet and the units are centimeters (cm). Only trees with DBH greater than 1.5 cm were sampled. Here are the diameters of a random sample of 40 of these trees: Data is available at CrunchIt! site: bcs.whfreeman.com/crunchit/ips6e On the left side of the worksheet page you will see a links to chapters; click on chapter 7, then select Exercise 25. (a) Use a histogram or stemplot and a boxplot to examine the distribution of DBHs. Include a Normal quantile plot if you have the necessary software. Write a careful description of the distribution. Variable: diameter 0 : : : : : : : 9 The boxplot, two histograms, and the stemplot suggest that the distribution is right skewed. I altered the second histogram to remove some of the detail and focus on the overall distribution shape. The Normal Quantile plot also confirms that the distribution is not normal.
5 (b) Is it appropriate to use the methods of this section to find a 95% confidence interval for the mean DBH of all trees in the Wade Tract? Explain why or why not (Hint: Look at normal quantile plot). The distribution of our population is not normal, but it does not have extreme outliers as is shown by the modified boxplot. Our sample size is 40, thus the Central Limit Theorem suggests that the distribution of the sample mean will be close enough to normal so that our probability calculations are accurate enough. (c) Report the mean with the margin of error and the confidence interval. Write a short summary describing the meaning of the confidence interval. Summary statistics: Column n Mean Variance Std. Dev. Std. Err. Median Range Min Max Q1 Q3 diameter
6 The degrees of freedom is 39, thus t * = ± ± (2.8000) (21.63, 32.95) Thus, we are 95% certain that our interval contains the true mean breast height diameter. (d) Do you think these results would apply to other similar trees in the same area? Give reasons for your answer Do you feel lucky? Children in a psychology study were asked to solve some puzzles and were then given feedback on their performance. Then they were asked to rate how luck played a role in determining their scores. 10 This variable was recorded on a 1 to 10 scale with 1 corresponding to very lucky and 10 corresponding to very unlucky. Here are the scores for 60 children: Data is available at CrunchIt! site: bcs.whfreeman.com/crunchit/ips6e On the left side of the worksheet page you will see a links to chapters; click on chapter 7, then select Exercise 25. (a) Use graphical methods to display the distribution. Describe any unusual characteristics. Do you think that these would lead you to hesitate before using the Normalitybased methods of this section? Ok, this is obviously not normally distributed, I do not need a normal quantile plot. This is an open and shut case. The result is very fascinating in that it seems to indicate we have two set of children here; maybe there are some issues on how each set of children sees life. Thus a statistician would try to find the correct category that would separate the children into their proper groups. But that is not the task here. The question however is can we use the confidence interval formula? For this to happen the distribution of xbar must be close to normal. Is a sample of 60 close enough for this data set? If you were to say no, I would totally understand your choice. However, one item that captures my eye is the symmetry of the distribution. Because of the symmetry it may be possible that a sample of 60 is large enough.
7 (b) Give a 95% confidence interval for the mean luck score. (c) The children in this study were volunteers whose parents agreed to have them participate in the study. To what extent do you think your results would apply to all similar children in this community?
Chapter 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 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 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 informationTwo Related Samples t Test
Two Related Samples t Test In this example 1 students saw five pictures of attractive people and five pictures of unattractive people. For each picture, the students rated the friendliness of the person
More informationChicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011
Chicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011 Name: Section: I pledge my honor that I have not violated the Honor Code Signature: This exam has 34 pages. You have 3 hours to complete this
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 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 informationGeneral 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 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 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 informationt Tests in Excel The Excel Statistical Master By Mark Harmon Copyright 2011 Mark Harmon
ttests in Excel By Mark Harmon Copyright 2011 Mark Harmon No part of this publication may be reproduced or distributed without the express permission of the author. mark@excelmasterseries.com www.excelmasterseries.com
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 informationSPSS for Exploratory Data Analysis Data used in this guide: studentp.sav (http://people.ysu.edu/~gchang/stat/studentp.sav)
Data used in this guide: studentp.sav (http://people.ysu.edu/~gchang/stat/studentp.sav) Organize and Display One Quantitative Variable (Descriptive Statistics, Boxplot & Histogram) 1. Move the mouse pointer
More information1.3 Measuring Center & Spread, The Five Number Summary & Boxplots. Describing Quantitative Data with Numbers
1.3 Measuring Center & Spread, The Five Number Summary & Boxplots Describing Quantitative Data with Numbers 1.3 I can n Calculate and interpret measures of center (mean, median) in context. n Calculate
More informationHYPOTHESIS TESTING WITH SPSS:
HYPOTHESIS TESTING WITH SPSS: A NONSTATISTICIAN S GUIDE & TUTORIAL by Dr. Jim Mirabella SPSS 14.0 screenshots reprinted with permission from SPSS Inc. Published June 2006 Copyright Dr. Jim Mirabella CHAPTER
More informationMultiple Linear Regression
Multiple Linear Regression A regression with two or more explanatory variables is called a multiple regression. Rather than modeling the mean response as a straight line, as in simple regression, it is
More informationChapter 23 Inferences About Means
Chapter 23 Inferences About Means Chapter 23  Inferences About Means 391 Chapter 23 Solutions to Class Examples 1. See Class Example 1. 2. We want to know if the mean battery lifespan exceeds the 300minute
More informationISyE 2028 Basic Statistical Methods  Fall 2015 Bonus Project: Big Data Analytics Final Report: Time spent on social media
ISyE 2028 Basic Statistical Methods  Fall 2015 Bonus Project: Big Data Analytics Final Report: Time spent on social media Abstract: The growth of social media is astounding and part of that success was
More informationData Mining Techniques Chapter 5: The Lure of Statistics: Data Mining Using Familiar Tools
Data Mining Techniques Chapter 5: The Lure of Statistics: Data Mining Using Familiar Tools Occam s razor.......................................................... 2 A look at data 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 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 informationPractice Problems and Exams
Practice Problems and Exams 1 The Islamic University of Gaza Faculty of Commerce Department of Economics and Political Sciences An Introduction to Statistics Course (ECOE 1302) Spring Semester 20092010
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 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 informationKSTAT MINIMANUAL. Decision Sciences 434 Kellogg Graduate School of Management
KSTAT MINIMANUAL Decision Sciences 434 Kellogg Graduate School of Management Kstat is a set of macros added to Excel and it will enable you to do the statistics required for this course very easily. To
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 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 informationWalk the Line Written by: Maryann Huey Drake University Maryann.Huey@drake.edu
Walk the Line Written by: Maryann Huey Drake University Maryann.Huey@drake.edu Overview of Lesson In this activity, students will conduct an investigation to collect data to determine how far students
More information7. Comparing Means Using ttests.
7. Comparing Means Using ttests. Objectives Calculate one sample ttests Calculate paired samples ttests Calculate independent samples ttests Graphically represent mean differences In this chapter,
More informationDongfeng Li. Autumn 2010
Autumn 2010 Chapter Contents Some statistics background; ; Comparing means and proportions; variance. Students should master the basic concepts, descriptive statistics measures and graphs, basic hypothesis
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 informationBA 275 Review Problems  Week 6 (10/30/0611/3/06) CD Lessons: 53, 54, 55, 56 Textbook: pp. 394398, 404408, 410420
BA 275 Review Problems  Week 6 (10/30/0611/3/06) CD Lessons: 53, 54, 55, 56 Textbook: pp. 394398, 404408, 410420 1. Which of the following will increase the value of the power in a statistical test
More informationSTAT 145 (Notes) Al Nosedal anosedal@unm.edu Department of Mathematics and Statistics University of New Mexico. Fall 2013
STAT 145 (Notes) Al Nosedal anosedal@unm.edu Department of Mathematics and Statistics University of New Mexico Fall 2013 CHAPTER 18 INFERENCE ABOUT A POPULATION MEAN. Conditions for Inference about mean
More informationa. mean b. interquartile range c. range d. median
3. Since 4. The HOMEWORK 3 Due: Feb.3 1. A set of data are put in numerical order, and a statistic is calculated that divides the data set into two equal parts with one part below it and the other part
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 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 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 informationCHAPTER 7 INTRODUCTION TO SAMPLING DISTRIBUTIONS
CHAPTER 7 INTRODUCTION TO SAMPLING DISTRIBUTIONS CENTRAL LIMIT THEOREM (SECTION 7.2 OF UNDERSTANDABLE STATISTICS) The Central Limit Theorem says that if x is a random variable with any distribution having
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 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 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 informationAn Introduction to Statistics Course (ECOE 1302) Spring Semester 2011 Chapter 10 TWOSAMPLE TESTS
The Islamic University of Gaza Faculty of Commerce Department of Economics and Political Sciences An Introduction to Statistics Course (ECOE 130) Spring Semester 011 Chapter 10 TWOSAMPLE TESTS Practice
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 informationSPSS/Excel Workshop 3 Summer Semester, 2010
SPSS/Excel Workshop 3 Summer Semester, 2010 In Assignment 3 of STATS 10x you may want to use Excel to perform some calculations in Questions 1 and 2 such as: finding Pvalues finding tmultipliers and/or
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 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 informationNovember 08, 2010. 155S8.6_3 Testing a Claim About a Standard Deviation or Variance
Chapter 8 Hypothesis Testing 8 1 Review and Preview 8 2 Basics of Hypothesis Testing 8 3 Testing a Claim about a Proportion 8 4 Testing a Claim About a Mean: σ Known 8 5 Testing a Claim About a Mean: σ
More informationDifference of Means and ANOVA Problems
Difference of Means and Problems Dr. Tom Ilvento FREC 408 Accounting Firm Study An accounting firm specializes in auditing the financial records of large firm It is interested in evaluating its fee structure,particularly
More informationSTAT 350 Practice Final Exam Solution (Spring 2015)
PART 1: Multiple Choice Questions: 1) A study was conducted to compare five different training programs for improving endurance. Forty subjects were randomly divided into five groups of eight subjects
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 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 informationUnit 26: Small Sample Inference for One Mean
Unit 26: Small Sample Inference for One Mean Prerequisites Students need the background on confidence intervals and significance tests covered in Units 24 and 25. Additional Topic Coverage Additional coverage
More informationPsychology 60 Fall 2013 Practice Exam Actual Exam: Next Monday. Good luck!
Psychology 60 Fall 2013 Practice Exam Actual Exam: Next Monday. Good luck! Name: 1. The basic idea behind hypothesis testing: A. is important only if you want to compare two populations. B. depends on
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 informationNCSS Statistical Software. OneSample TTest
Chapter 205 Introduction This procedure provides several reports for making inference about a population mean based on a single sample. These reports include confidence intervals of the mean or median,
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 informationComparing Means in Two Populations
Comparing Means in Two Populations Overview The previous section discussed hypothesis testing when sampling from a single population (either a single mean or two means from the same population). Now we
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 informationOpgaven Onderzoeksmethoden, Onderdeel Statistiek
Opgaven Onderzoeksmethoden, Onderdeel Statistiek 1. What is the measurement scale of the following variables? a Shoe size b Religion c Car brand d Score in a tennis game e Number of work hours per week
More informationMONT 107N Understanding Randomness Solutions For Final Examination May 11, 2010
MONT 07N Understanding Randomness Solutions For Final Examination May, 00 Short Answer (a) (0) How are the EV and SE for the sum of n draws with replacement from a box computed? Solution: The EV is n times
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
STT315 Practice Ch 57 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) The length of time a traffic signal stays green (nicknamed
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 informationEXAM #1 (Example) Instructor: Ela Jackiewicz. Relax and good luck!
STP 231 EXAM #1 (Example) Instructor: Ela Jackiewicz Honor Statement: I have neither given nor received information regarding this exam, and I will not do so until all exams have been graded and returned.
More informationIntroduction. Hypothesis Testing. Hypothesis Testing. Significance Testing
Introduction Hypothesis Testing Mark Lunt Arthritis Research UK Centre for Ecellence in Epidemiology University of Manchester 13/10/2015 We saw last week that we can never know the population parameters
More informationChapter 13 Introduction to Linear Regression and Correlation Analysis
Chapter 3 Student Lecture Notes 3 Chapter 3 Introduction to Linear Regression and Correlation Analsis Fall 2006 Fundamentals of Business Statistics Chapter Goals To understand the methods for displaing
More informationP(every one of the seven intervals covers the true mean yield at its location) = 3.
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
More information1.5 Oneway Analysis of Variance
Statistics: Rosie Cornish. 200. 1.5 Oneway Analysis of Variance 1 Introduction Oneway analysis of variance (ANOVA) is used to compare several means. This method is often used in scientific or medical experiments
More informationHYPOTHESIS TESTING: POWER OF THE TEST
HYPOTHESIS TESTING: POWER OF THE TEST The first 6 steps of the 9step test of hypothesis are called "the test". These steps are not dependent on the observed data values. When planning a research project,
More information13: Additional ANOVA Topics. Post hoc Comparisons
13: Additional ANOVA Topics Post hoc Comparisons ANOVA Assumptions Assessing Group Variances When Distributional Assumptions are Severely Violated KruskalWallis Test Post hoc Comparisons In the prior
More informationExercise 1.12 (Pg. 2223)
Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.
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 informationconsider the number of math classes taken by math 150 students. how can we represent the results in one number?
ch 3: numerically summarizing data  center, spread, shape 3.1 measure of central tendency or, give me one number that represents all the data consider the number of math classes taken by math 150 students.
More informationPaired TTest. Chapter 208. Introduction. Technical Details. Research Questions
Chapter 208 Introduction This procedure provides several reports for making inference about the difference between two population means based on a paired sample. These reports include confidence intervals
More informationUnbeknownst to us, the entire population consists of 5 cloned sheep with ages 10, 11, 12, 13, 14 months.
Activity #14: Sampling distributions and the Central Limit Theorem So far, this unit has focused on distributions of discrete and continuous random variables. In this activity, we ll investigate sampling
More informationChapter 2 Probability Topics SPSS T tests
Chapter 2 Probability Topics SPSS T tests Data file used: gss.sav In the lecture about chapter 2, only the OneSample T test has been explained. In this handout, we also give the SPSS methods to perform
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 informationAP Statistics: Syllabus 1
AP Statistics: Syllabus 1 Scoring Components SC1 The course provides instruction in exploring data. 4 SC2 The course provides instruction in sampling. 5 SC3 The course provides instruction in experimentation.
More informationStats for Strategy Fall 2012 FirstDiscussion Handout: Stats Using Calculators and MINITAB
Stats for Strategy Fall 2012 FirstDiscussion Handout: Stats Using Calculators and MINITAB DIRECTIONS: Welcome! Your TA will help you apply your Calculator and MINITAB to review Business Stats, and will
More informationBasic Statistics and Data Analysis for Health Researchers from Foreign Countries
Basic Statistics and Data Analysis for Health Researchers from Foreign Countries Volkert Siersma siersma@sund.ku.dk The Research Unit for General Practice in Copenhagen Dias 1 Content Quantifying association
More informationAP Statistics 2010 Scoring Guidelines
AP Statistics 2010 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 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 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 informationDescribing Populations Statistically: The Mean, Variance, and Standard Deviation
Describing Populations Statistically: The Mean, Variance, and Standard Deviation BIOLOGICAL VARIATION One aspect of biology that holds true for almost all species is that not every individual is exactly
More informationOutline. Definitions Descriptive vs. Inferential Statistics The ttest  Onesample ttest
The ttest Outline Definitions Descriptive vs. Inferential Statistics The ttest  Onesample ttest  Dependent (related) groups ttest  Independent (unrelated) groups ttest Comparing means Correlation
More informationA) 0.1554 B) 0.0557 C) 0.0750 D) 0.0777
Math 210  Exam 4  Sample Exam 1) What is the pvalue for testing H1: µ < 90 if the test statistic is t=1.592 and n=8? A) 0.1554 B) 0.0557 C) 0.0750 D) 0.0777 2) The owner of a football team claims that
More information1. How different is the t distribution from the normal?
Statistics 101 106 Lecture 7 (20 October 98) c David Pollard Page 1 Read M&M 7.1 and 7.2, ignoring starred parts. Reread M&M 3.2. The effects of estimated variances on normal approximations. tdistributions.
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 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 informationDiagrams and Graphs of Statistical Data
Diagrams and Graphs of Statistical Data One of the most effective and interesting alternative way in which a statistical data may be presented is through diagrams and graphs. There are several ways in
More informationTHE PROCESS CAPABILITY ANALYSIS  A TOOL FOR PROCESS PERFORMANCE MEASURES AND METRICS  A CASE STUDY
International Journal for Quality Research 8(3) 399416 ISSN 18006450 Yerriswamy Wooluru 1 Swamy D.R. P. Nagesh THE PROCESS CAPABILITY ANALYSIS  A TOOL FOR PROCESS PERFORMANCE MEASURES AND METRICS 
More information12.5: CHISQUARE GOODNESS OF FIT TESTS
125: ChiSquare Goodness of Fit Tests CD121 125: CHISQUARE GOODNESS OF FIT TESTS In this section, the χ 2 distribution is used for testing the goodness of fit of a set of data to a specific probability
More informationPart 3. Comparing Groups. Chapter 7 Comparing Paired Groups 189. Chapter 8 Comparing Two Independent Groups 217
Part 3 Comparing Groups Chapter 7 Comparing Paired Groups 189 Chapter 8 Comparing Two Independent Groups 217 Chapter 9 Comparing More Than Two Groups 257 188 Elementary Statistics Using SAS Chapter 7 Comparing
More informationMinitab Tutorials for Design and Analysis of Experiments. Table of Contents
Table of Contents Introduction to Minitab...2 Example 1 OneWay ANOVA...3 Determining Sample Size in Oneway ANOVA...8 Example 2 Twofactor Factorial Design...9 Example 3: Randomized Complete Block Design...14
More informationChapter 1: Looking at Data Section 1.1: Displaying Distributions with Graphs
Types of Variables Chapter 1: Looking at Data Section 1.1: Displaying Distributions with Graphs Quantitative (numerical)variables: take numerical values for which arithmetic operations make sense (addition/averaging)
More informationNCSS Statistical Software
Chapter 06 Introduction This procedure provides several reports for the comparison of two distributions, including confidence intervals for the difference in means, twosample ttests, the ztest, the
More informationChapter 1: Exploring Data
Chapter 1: Exploring Data Chapter 1 Review 1. As part of survey of college students a researcher is interested in the variable class standing. She records a 1 if the student is a freshman, a 2 if the student
More informationUnderstanding Confidence Intervals and Hypothesis Testing Using Excel Data Table Simulation
Understanding Confidence Intervals and Hypothesis Testing Using Excel Data Table Simulation Leslie Chandrakantha lchandra@jjay.cuny.edu Department of Mathematics & Computer Science John Jay College of
More informationUnit 31: OneWay ANOVA
Unit 31: OneWay ANOVA Summary of Video A vase filled with coins takes center stage as the video begins. Students will be taking part in an experiment organized by psychology professor John Kelly in which
More informationStatistics Review PSY379
Statistics Review PSY379 Basic concepts Measurement scales Populations vs. samples Continuous vs. discrete variable Independent vs. dependent variable Descriptive vs. inferential stats Common analyses
More information