# The Importance of Statistics Education

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 The Importance of Statistics Education Professor Jessica Utts Department of Statistics University of California, Irvine

2 Outline of Talk What is Statistics? Four examples of statistical decisions in daily life why statistics education matters Introducing Statistics into grades K-12 in US Previous attempts Common Core State Standards; revisit examples More examples of statistics in daily life (as time permits)

3 What is Statistics? Decisions or predictions are often based on data numbers in context. These decisions or predictions would be easy if the data always sent a clear message, but the message is often obscured by variability. Statistics provides tools for describing variability in data and for making informed decisions that take it into account. Source: The Common Core,

4 Decisions: Example 1 You are offered jobs as a manager at two companies. One reports that the average salary for managerial positions is \$95,000 and the other reports that the median salary for managerial positions is \$70,000. What do these numbers mean and can they help you choose which job to take? What more do you need to know? Students should be able to answer these questions by Grade 6.

5 Decisions: Example 2 Headline:Yogurt Reduces High Blood Pressure, says a New Study Study tracked 2100 people for 14 years; they recorded what they ate. Those who ate yogurt were 31% less likely to develop high blood pressure. Questions and Decisions: If you have high blood pressure, will eating yogurt help reduce it? What more do you need to know about the study?

6 Decisions: Example 3 You are planning to take a trip in a few months. You go to a hotel website and are offered two choices: Pay \$85 a night now, non-refundable. Pay \$100 a night when you take the trip; you don t pay if you don t go. Questions and Decisions: How sure do you have to be that you will actually go, to make the advance purchase the better choice?

7 Decisions: Example 4 You are a middle-aged man and your total cholesterol level is 200 mg/dl. Your doctor wants you to take statin drugs. Questions and Decisions: What proportion of middle-aged men have total cholesterol that high or higher? Are there risks from taking the drug that outweigh the benefits?

8 The Importance of Statistics My ideal world: All educated citizens should be able to answer those and similar questions by the time they graduate from secondary school. Basic literacy in statistics and probability does not require advanced mathematics. How do we get there?

9 New Curriculum in the US Common Core Will be discussed in the round table Guidelines for each grade from K-12

10 GAISE Report 2005: American Statistical Association (ASA) report Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report in 2 parts K to 12 and College K-12 report has 108 pages of detailed guidelines on teaching statistics in K-12, with examples, teaching strategies, and so on

11 Common Core for grades K to 5 Use data displays to ask and answer questions about data. Understand measures used to summarize data, including the mean, median, interquartile range, and mean absolute deviation, and Use these measures to compare datasets.

12 Remember Decision Example 1 You are offered jobs as a manager at two companies. One reports that the average salary for managerial positions is \$95,000 and the other reports that the median salary for managerial positions is \$70,000. After Grade 5, students should understand: Average salary = mean = amount everyone would get if they divided the salary money equally, but it is greatly affected by one or more very high salaries. Median salary is the value that half of the salaries are at or above and half of the salaries are at or below.

13 Teaching Mean and Median to Young Children (Example from GAISE) Data = Number of letters in children s names. To find Median name length: Line up all of the children in order, from shortest name to longest name. Have one child at each end sit down. Continue until one child is left standing. To find Mean name length: Give each child a block for each letter in their name. Put all of the blocks together; divide equally.

14 Common Core for Grades 6 to 8 Statistics and Probability Topics Develop understanding of statistical variability Summarize and describe distributions Use random sampling to draw inferences about a population Draw informal comparative inferences about two populations Investigate chance processes and develop, use and evaluate probability models Investigate patterns of association in bivariate data

15 Comparing Data Sets using Mean/Median If 1 st company has an average salary of \$95,000 and 2 nd company has a median salary of \$70,000, could the typical employee be better off with the 2 nd company? Yes! Suppose the 1 st company has these 10 salaries: 9 people earning \$50,000 each = \$450,000 The top manager (CEO) earning \$500,000 Then the mean is \$950,000/10 = \$95,000 But the median and typical salary is \$50,000 In this example, medians are \$50,000 (1 st company) and \$70,000 (2 nd company). 2 nd company is better. To compare, we need information about the distribution!

16 More on Decision Example 1 In Grades 6 to 8 students should learn: The mean of \$95,000 and median of \$70,000 don t provide enough information to decide. You need to know the distribution of salaries at each company You at least need to know if there are outliers In might also be helpful to see some bivariate data, such as: Plot of salary versus years of experience Comparative salaries for men and women

17 Remember Decision Example 2 Headline:Yogurt Reduces High Blood Pressure, says a New Study Study tracked 2100 people for 14 years; they recorded what they ate. Those who ate yogurt were 31% less likely to develop high blood pressure. Questions and Decisions: If you have high blood pressure, will eating yogurt help reduce it? What more do you need to know about the study?

18 Common Core for Secondary School (Grades 9 to 12) Four broad categories (with codes): (ID) Interpreting categorical and quantitative data (including linear models) (IC) Making inferences and justifying conclusions (CP) Conditional probability and the rules of probability (MD) Using probability to make decisions

19 Concluding Cause and Effect Randomized experiment The researchers Create differences in groups Observe differences in response Example: Randomly assign people to eat yogurt or not, measure and compare blood pressure. Observational study The researchers Observe differences in groups Observe differences in response Example: Ask people if they eat yogurt or not, measure and compare blood pressure.

20 Explanatory, Response and Confounding Variables Explanatory variable defines the groups People who ate yogurt regularly or did not Response variable is the outcome of interest Response for each person = blood pressure Confounding variables Are related to the explanatory variable, and Might affec the response variable. Yogurt group might be more health conscious, better exercise, better diet, etc.

21 Observational Studies, Randomized Experiments and Confounding Observational studies: confounding variables can t be separated from the explanatory variable in affecting the outcome. Cannot conclude that changes in the explanatory variable cause a change in the response. In randomized experiments, random assignment should even out confounding variables across groups, so we can conclude cause and effect. Yogurt study: Clearly an observational study (tracked people for 14 years), so we cannot conclude that yogurt causes lower blood pressure. Difference could be due to effect on blood pressure of healthier diet, exercise, etc.

22 Example of a Randomized Experiment The Abecedarian Project (University of North Carolina) randomly assigned poor infants to receive full-time, educational child care (57 children), or not (54 children). Kept track into adulthood. Some major findings at age 30 those with child care were: Almost 4 times as likely to graduate from college (23% vs 6%) More likely to have been employed consistently over the previous two years (74% vs 53%) Much less likely to be teen-aged parents (26% vs 45%) Randomized experiment, so can conclude that the child care caused the differences.

23 Remember Decision Example 3 You are planning to take a trip in a few months. You go to a hotel website and are offered two choices: Pay \$85 a night now, non-refundable Pay \$100 a night when you take the trip; you don t pay if you don t go. Questions and Decisions: How sure do you have to be that you will actually go, to make the advance purchase the better choice?

24 Common Core for Secondary School (Grades 9 to 12) Four broad categories (with codes): (ID) Interpreting categorical and quantitative data (including linear models) (IC) Making inferences and justifying conclusions (CP) Conditional probability and the rules of probability (MD) Using probability to make decisions

25 Expected Value Expected value is the weighted average of the possible values, with probabilities as weights = Sum of (value probability) With advance purchase option there is one value: \$85 with probability 1.0 Without advance purchase option: Define p = probability you will go on the trip Two possible values: \$100 if you go, \$0 if not Probability distribution: Value \$100 \$0 Prob. p 1 p

26 Expected Value (EV) of Cost of Hotel Room With advance purchase: \$85 with probability 1.0, so EV = \$85. Without advance purchase: EV = \$100p + \$0(1 p) = \$100p When is \$100p < \$85? If p < So don t buy advance purchase if p <.85.

27 Remember Decision Example 4 You are a middle-aged man and your total cholesterol level is 200 mg/dl. Your doctor wants you to take statin drugs. Questions and Decisions: What proportion of middle-aged men have total cholesterol that high or higher? Are there risks from taking the drug that outweigh the benefits?

28 The Relevant Specific Standard Standard ID4: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

29 Cholesterol Example What proportion of middle-aged men have borderline high cholesterol = 200 or more? High cholesterol is 240 or more. What proportion have high cholesterol? From previous data, middle-aged men s cholesterol levels are approximately normally distributed with mean of 222 mg and standard deviation of 37 mg. Excel, free software and websites can find probabilities for normal distributions.

30 Picture for Cholesterol Example Thanks to Brigitte Baldi, UC Irvine for the data and picture. Note that over 31% have high cholesterol, and a total of over 72% have borderline high of over 200! Should they all take drugs?

31 More Examples of Importance of Understanding Statistics in Daily Life The problem of multiple testing Weighing competing risks: Risk, relative risk, absolute risk Poor intuition about probability

32 Real Relationships or Chance Does eating cereal produce boys? Headline in New Scientist: Breakfast cereal boosts chances of conceiving boys Numerous other media stories of this study. Study in Proc. of Royal Soc. B showed of women who ate cereal, 59% had boys, of women who didn t, 43% had boys. Problem #1: Headline implies eating cereal causes change in probability, but this was an observational study. Confounding likely!

33 The Problem of Multiple Testing The study investigated 132 foods the women ate, at 2 time periods for each food = 264 possible tests! By chance alone, some food would show a difference in birth rates for boys and girls. Main issue: Selective reporting of results when many relationships are examined, not adjusted for multiple testing. Quite likely that there are false positive results.

34 Competing Risks: Avoiding Risk May Put You in Danger In 1995, UK Committee on Safety of Medicines issued warning that new oral contraceptive pills increased the risk of potentially life threatening blood clots in the legs or lungs by twofold that is, by 100% over the old pills Letters to 190,000 medical practitioners; emergency announcement to the media Many women stopped taking pills.

35 Clearly there is increased risk, so what s the problem with women stopping pills? Probable consequences: Increase of 13,000 abortions the following year Similar increase in births, especially large for teens Additional \$70 million cost to National Health Service for abortions alone Additional deaths and complications probably far exceeded pill risk.

36 Considerations about Risk Changing a behavior based on one risk may increase overall risk of a problem. Think about trade offs. Find out what the absolute risk is, and consider risk in terms of additional number at risk Example: Suppose a behavior doubles risk of cancer Brain tumor: About 7 in 100,000 new cases per year, so adds about 7 cases per 100,000 per year. Lung cancer: About 75 in 100,000 new cases per year, so adds 75 per 100,000, more than 10 times as many!

37 Medical Test for a disease Medical Test is accurate 90% of the time 1% of the population have the disease Test positive Test negative Total Disease 900 (90%) (1%) No disease 9,900 (10%) 89,100 99,000 Total 10,800 89, ,000 Probability of disease, given positive test = 900/10800 = 8.3%

38 Other Probability Distortions Coincidences have higher probability than people think, because there are so many of us and so many ways they can occur. Low risk, scary events in the news are perceived to have higher probability than they have (readily brought to mind). So are detailed scenarios. High risk events where we think we have control are perceived to have lower probability than they have. People place less credence on data that conflict with their beliefs than on data that support them.

39 Probability and Intuition Lessons Examples of Consequences in daily life: Assessing probability in criminal cases Lawyers will provide detailed scenarios because judges assign higher probabilities Extended warranties and other insurance Expected value favors the seller Gambling and lotteries Again, average gain per ticket is negative Poor decisions (e.g. driving versus flying)

40 Recommendations for Training Future Teachers Statistics and Math Education Departments must work together to create Statistics training for teachers that: Focus on concepts rather than techniques Teach future math teachers why statistics is an important topic for children to learn. Teachers beliefs about statistics are as important as content. Integrate statistics topics with ideas for how to teach them in K-12 (content with pedagogy). Focus on the 4-step process outlined in the GAISE Report: Ask question, design and collect data, analyze data, interpret results.

41 Recommendations for Current Teachers Already there are many resources available. Administrators need to provide information and opportunities for teachers to utilize them. Professional organizations (ASA, MAA, NCTM) must work together to offer and publicize the existence of training materials, workshops, etc. As with new teachers, attitude toward statistics is crucial!

42 Conclusions Statistics and probability are important for making decisions in life Statistics should be taught to all students in primary and secondary school Statistics is not mathematics. The methods sometimes uses mathematics, but the basic ideas do not require advanced math. We need better teacher training in statistics and probability, with focus on concepts and importance.

43 Acknowledgements Thanks for these people for help with some content: Christine Franklin, University of Georgia Roxy Peck, California State Polytechnic University Brigitte Baldi, University of California, Irvine

44 QUESTIONS? Contact info:

### C. The null hypothesis is not rejected when the alternative hypothesis is true. A. population parameters.

Sample Multiple Choice Questions for the material since Midterm 2. Sample questions from Midterms and 2 are also representative of questions that may appear on the final exam.. A randomly selected sample

### COMMON CORE STATE STANDARDS FOR

COMMON CORE STATE STANDARDS FOR Mathematics (CCSSM) High School Statistics and Probability Mathematics High School Statistics and Probability Decisions or predictions are often based on data numbers in

### What is the purpose of this document? What is in the document? How do I send Feedback?

This document is designed to help North Carolina educators teach the Common Core (Standard Course of Study). NCDPI staff are continually updating and improving these tools to better serve teachers. Statistics

### Section 5.1 Randomness, Probability, and Simulation. The Idea of Probability

Section 5.1 Randomness, Probability, and Simulation The Idea of Probability Chance behavior is unpredictable in the short run, but has a regular and predictable pattern in the long run. The says that if

### How Long are the Names in my Class?

How Long are the Names in my Class? Overview of Lesson During the first week of school, a third-grade teacher is trying to help her students learn one another s names by playing various games. During one

### HIGH SCHOOL TEACHERS REASONING ABOUT DATA ANALYSIS IN A DYNAMICS STATISTICAL ENVIRONMENT

HIGH SCHOOL TEACHERS REASONING ABOUT DATA ANALYSIS IN A DYNAMICS STATISTICAL ENVIRONMENT Santiago Inzunsa and José A. Juárez Universidad Autónoma de Sinaloa, México sinzunza@uas.uasnet.mx In this article

### Pie Charts. proportion of ice-cream flavors sold annually by a given brand. AMS-5: Statistics. Cherry. Cherry. Blueberry. Blueberry. Apple.

Graphical Representations of Data, Mean, Median and Standard Deviation In this class we will consider graphical representations of the distribution of a set of data. The goal is to identify the range of

### South Carolina College- and Career-Ready (SCCCR) Probability and Statistics

South Carolina College- and Career-Ready (SCCCR) Probability and Statistics South Carolina College- and Career-Ready Mathematical Process Standards The South Carolina College- and Career-Ready (SCCCR)

### STATISTICS 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

### How Long is 30 Seconds?

How Long is 30 Seconds? Debra L. Hydorn University of Mary Washington dhydorn@umw.edu Published: Febuary 2012 Overview of Lesson In this activity students conduct an investigation to assess how well individuals

### Cents and the Central Limit Theorem Overview of Lesson GAISE Components Common Core State Standards for Mathematical Practice

Cents and the Central Limit Theorem Overview of Lesson In this lesson, students conduct a hands-on demonstration of the Central Limit Theorem. They construct a distribution of a population and then construct

### Versions 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

### Introduction to the Practice of Statistics Fifth Edition Moore, McCabe

Introduction to the Practice of Statistics Fifth Edition Moore, McCabe Section 1.3 Homework Answers 1.80 If you ask a computer to generate "random numbers between 0 and 1, you uniform will get observations

### 3. Data Analysis, Statistics, and Probability

3. Data Analysis, Statistics, and Probability Data and probability sense provides students with tools to understand information and uncertainty. Students ask questions and gather and use data to answer

### Guest Editorial Common Core State Standards and the Future of Teacher Preparation in Statistics

The Mathematics Educator 2013 Vol. 22, No. 2, 3 10 Guest Editorial Common Core State Standards and the Future of Teacher Preparation in Statistics Christine Franklin In our data-centric world, statistics

### By dividing the frequency by the total number of females.

Example 1: Conditional Relative Frequencies Recall the two way table from the previous lesson: a) How is relative frequency calculated? By dividing the frequency by the total observations b) How could

### WELCOME TO STATISTICS AND PROBABILITY FOR MIDDLE-SCHOOL MATH TEACHERS: ADDRESSING THE COMMON CORE. Karen Togliatti, Curriculum and PD Specialist

WELCOME TO STATISTICS AND PROBABILITY FOR MIDDLE-SCHOOL MATH TEACHERS: ADDRESSING THE COMMON CORE Karen Togliatti, Curriculum and PD Specialist Mathematics Progressions To see where the Statistics and

### The Importance of Statistics

The Importance of Statistics My ideal world: All educated citizens should be able to answer those and similar questions by the time they graduate from secondary school. Basic literacy in statistics and

### 5.1.1 The Idea of Probability

5.1.1 The Idea of Probability Chance behavior is unpredictable in the short run but has a regular and predictable pattern in the long run. This remarkable fact is the basis for the idea of probability.

### Problem of the Month Through the Grapevine

The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core State Standards: Make sense of problems

### Carolyn Anderson & Youngshil Paek (Slides created by Shuai Sam Wang) Department of Educational Psychology University of Illinois at Urbana-Champaign

Carolyn Anderson & Youngshil Paek (Slides created by Shuai Sam Wang) Department of Educational Psychology University of Illinois at Urbana-Champaign Key Points 1. Data 2. Variable 3. Types of data 4. Define

### Exam 2 Study Guide and Review Problems

Exam 2 Study Guide and Review Problems Exam 2 covers chapters 4, 5, and 6. You are allowed to bring one 3x5 note card, front and back, and your graphing calculator. Study tips: Do the review problems below.

### Suggested Time Frame Time Frame: 4 th Six Weeks Suggested Duration: 13 days. Vertical Alignment Expectations

Title Scatterplots and Data Analysis Big Ideas/Enduring Understandings The student will understand how patterns are used when comparing two quantities. Suggested Time Frame Time Frame: 4 th Six Weeks Suggested

### Session 7 Bivariate Data and Analysis

Session 7 Bivariate Data and Analysis Key Terms for This Session Previously Introduced mean standard deviation New in This Session association bivariate analysis contingency table co-variation least squares

### PISA Style Scientific Literacy Question

PISA Style Scientific Literacy Question Read the text about Statins Statins are drugs which stop the liver producing too much cholesterol. Doctors say that many heart attacks and strokes are prevented

### Math 140 (4,5,6) Sample Exam II Fall 2011

Math 140 (4,5,6) Sample Exam II Fall 2011 Provide an appropriate response. 1) In a sample of 10 randomly selected employees, it was found that their mean height was 63.4 inches. From previous studies,

### MAT 118 DEPARTMENTAL FINAL EXAMINATION (written part) REVIEW. Ch 1-3. One problem similar to the problems below will be included in the final

MAT 118 DEPARTMENTAL FINAL EXAMINATION (written part) REVIEW Ch 1-3 One problem similar to the problems below will be included in the final 1.This table presents the price distribution of shoe styles offered

### Margin 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

### GES3 Solve problems using quantitative reasoning.

GES3 Solve problems using quantitative reasoning. MATH1010 Foundations of Math Semester: FALL 2013 REPORT DATE: 1/13/2014 Foundations of Math is an introductory level mathematics course that serves non-

### p1^ = 0.18 p2^ = 0.12 A) 0.150 B) 0.387 C) 0.300 D) 0.188 3) n 1 = 570 n 2 = 1992 x 1 = 143 x 2 = 550 A) 0.270 B) 0.541 C) 0.520 D) 0.

Practice for chapter 9 and 10 Disclaimer: the actual exam does not mirror this. This is meant for practicing questions only. The actual exam in not multiple choice. Find the number of successes x suggested

### 10-3 Measures of Central Tendency and Variation

10-3 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.

### Chapter 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)

### Standard 12: The student will explain and evaluate the financial impact and consequences of gambling.

TEACHER GUIDE 12.1 GAMBLING PAGE 1 Standard 12: The student will explain and evaluate the financial impact and consequences of gambling. Risky Business Priority Academic Student Skills Personal Financial

### Testing Scientific Explanations (In words slides page 7)

Testing Scientific Explanations (In words slides page 7) Most people are curious about the causes for certain things. For example, people wonder whether exercise improves memory and, if so, why? Or, we

### Section 14 Simple Linear Regression: Introduction to Least Squares Regression

Slide 1 Section 14 Simple Linear Regression: Introduction to Least Squares Regression There are several different measures of statistical association used for understanding the quantitative relationship

### Mind on Statistics. Chapter 2

Mind on Statistics Chapter 2 Sections 2.1 2.3 1. Tallies and cross-tabulations are used to summarize which of these variable types? A. Quantitative B. Mathematical C. Continuous D. Categorical 2. The table

### Models of a Vending Machine Business

Math Models: Sample lesson Tom Hughes, 1999 Models of a Vending Machine Business Lesson Overview Students take on different roles in simulating starting a vending machine business in their school that

### Rigorous Curriculum Design Authentic Performance Tasks

Rigorous Curriculum Design Authentic Performance Tasks 1 of 14 Subject Grade/Course Unit of Study Duration of Unit Math 8 th Grade/ Math Unit 6 Scatter plots and statistics 3-4 Weeks Engaging Scenario

### Statistical Significance and Bivariate Tests

Statistical Significance and Bivariate Tests BUS 735: Business Decision Making and Research 1 1.1 Goals Goals Specific goals: Re-familiarize ourselves with basic statistics ideas: sampling distributions,

### RUTHERFORD HIGH SCHOOL Rutherford, New Jersey COURSE OUTLINE STATISTICS AND PROBABILITY

RUTHERFORD HIGH SCHOOL Rutherford, New Jersey COURSE OUTLINE STATISTICS AND PROBABILITY I. INTRODUCTION According to the Common Core Standards (2010), Decisions or predictions are often based on data numbers

### The Idea of Probability

AP Statistics 5.1 Reading Guide Name Directions: Read the following pages and then answer the questions at the end. We ll have a short mini-quiz over this material (for Mastery) when we return from Thanksgiving

### Lesson Plan #3. Simulations

Lesson Plan #3 Simulations Grade: 7 th grade Subject: Mathematics About the class: Standards: Objectives: - 20 students- 11 boys, 9 girls - 7 students are special education students - One-teach, one-assist

### Chapter 3: Producing Data (Part 1) Dr. Nahid Sultana

Chapter 3: Producing Data (Part 1) Dr. Nahid Sultana Chapter 3: Producing Data Introduction 3.1 Design of Experiments 3.2 Sampling Design 3.3 Toward Statistical Inference 3.4 Ethics Introduction Anecdotal

### Armspans. Published: August 2012. Debra L. Hydorn University of Mary Washington

Armspans Debra L. Hydorn University of Mary Washington dhydorn@umw.edu Published: August 2012 Overview of Lesson In this activity students conduct an investigation to compare the arm span lengths of the

### Mathematics. GSE Algebra II/ Advanced Algebra Unit 7: Inferences & Conclusions from Data

Georgia Standards of Excellence Curriculum Frameworks Mathematics GSE Algebra II/ Advanced Algebra Unit 7: Inferences & Conclusions from Data These materials are for nonprofit educational purposes only.

### 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

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

### CHAPTER 8 TESTING HYPOTHESES. Most of the information presented in the first seven chapters of this text has focused on

CHAPTER 8 TESTING HYPOTHESES Most of the information presented in the first seven chapters of this text has focused on the theoretical and mathematical foundations for a range of statistics beginning with

### Bock-Ch13 Review.docx

Multiple Choice 1. Which of the following situations qualifies as an observational study? (A) The girls at your high school are surveyed to determine if they believe there is any sexual stereotyping in

### Measurement with Ratios

Grade 6 Mathematics, Quarter 2, Unit 2.1 Measurement with Ratios Overview Number of instructional days: 15 (1 day = 45 minutes) Content to be learned Use ratio reasoning to solve real-world and mathematical

### Test 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

### Lesson 15.1 Skills Practice

Lesson 15.1 Skills Practice Name Date School Spirit and Scatter Plots Using Scatter Plots to Display and Analyze Two-Variable Relationships Vocabulary Write a definition for each term in your own words.

### Sample 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

### Lesson 18 Student Outcomes Lesson Notes

Lesson 18 Analyzing Residuals Student Outcomes Students use a graphing calculator to construct the residual plot for a given data set. Students use a residual plot as an indication of whether or not the

PROBLEM SET 1 For the first three answer true or false and explain your answer. A picture is often helpful. 1. Suppose the significance level of a hypothesis test is α=0.05. If the p-value of the test

### HISTOGRAMS, CUMULATIVE FREQUENCY AND BOX PLOTS

Mathematics Revision Guides Histograms, Cumulative Frequency and Box Plots Page 1 of 25 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier HISTOGRAMS, CUMULATIVE FREQUENCY AND BOX PLOTS

### Lesson 2: Calculating Probabilities of Events Using Two- Way Tables

: Calculating Probabilities of Events Using Two- Way Tables Student Outcomes Students calculate probabilities given a two-way table of data. Students construct a hypothetical 1000 two-way table given probability

### Regression. In this class we will:

AMS 5 REGRESSION Regression The idea behind the calculation of the coefficient of correlation is that the scatter plot of the data corresponds to a cloud that follows a straight line. This idea can be

### Cell Phone Impairment?

Cell Phone Impairment? Overview of Lesson This lesson is based upon data collected by researchers at the University of Utah (Strayer and Johnston, 2001). The researchers asked student volunteers (subjects)

### Data Types. 1. Continuous 2. Discrete quantitative 3. Ordinal 4. Nominal. Figure 1

Data Types By Tanya Hoskin, a statistician in the Mayo Clinic Department of Health Sciences Research who provides consultations through the Mayo Clinic CTSA BERD Resource. Don t let the title scare you.

### Statistics in the Middle Grades:

contemporary curriculum issues Gary Kader and Jim Mamer Statistics in the Middle Grades: Understanding Center and Spread Gary Kader, gdk@math.appstate.edu, is a professor of mathematical sciences at Appalachian

### Chapter 10 - Practice Problems 1

Chapter 10 - Practice Problems 1 1. A researcher is interested in determining if one could predict the score on a statistics exam from the amount of time spent studying for the exam. In this study, the

### AP Statistics Final Examination Multiple-Choice Questions Answers in Bold

AP Statistics Final Examination Multiple-Choice Questions Answers in Bold Name Date Period Answer Sheet: Multiple-Choice Questions 1. A B C D E 14. A B C D E 2. A B C D E 15. A B C D E 3. A B C D E 16.

### Mind on Statistics. Chapter 12

Mind on Statistics Chapter 12 Sections 12.1 Questions 1 to 6: For each statement, determine if the statement is a typical null hypothesis (H 0 ) or alternative hypothesis (H a ). 1. There is no difference

### Topic (2) Sampling and Experimental Design. Experimental (or Sampling) Unit is the object or event from which the measurements are taken

Topic (2) Sampling and Experimental Design 2-1 Topic (2) Sampling and Experimental Design Some Definitions Experimental (or Sampling) Unit is the object or event from which the measurements are taken e.g.

### How to interpret scientific & statistical graphs

How to interpret scientific & statistical graphs Theresa A Scott, MS Department of Biostatistics theresa.scott@vanderbilt.edu http://biostat.mc.vanderbilt.edu/theresascott 1 A brief introduction Graphics:

### Experimental Designs leading to multiple regression analysis

Experimental Designs leading to multiple regression analysis 1. (Randomized) designed experiments. 2. Randomized block experiments. 3. Observational studies: probability based sample surveys 4. Observational

### Personal Financial Literacy

Personal Financial Literacy 7 Unit Overview Being financially literate means taking responsibility for learning how to manage your money. In this unit, you will learn about banking services that can help

### Mean, Median, and Mode

DELTA MATH SCIENCE PARTNERSHIP INITIATIVE M 3 Summer Institutes (Math, Middle School, MS Common Core) Mean, Median, and Mode Hook Problem: To compare two shipments, five packages from each shipment were

### Fairfield Public Schools

Mathematics Fairfield Public Schools AP Statistics AP Statistics BOE Approved 04/08/2014 1 AP STATISTICS Critical Areas of Focus AP Statistics is a rigorous course that offers advanced students an opportunity

### Descriptive Statistics and Measurement Scales

Descriptive Statistics 1 Descriptive Statistics and Measurement Scales Descriptive statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample

### Hypothesis Testing: Significance

STAT 101 Dr. Kari Lock Morgan Hypothesis Testing: Significance SECTION 4.3, 4.5 Significance level (4.3) Statistical conclusions (4.3) Type I and II errors (4.3) Statistical versus practical significance

### JUROR QUESTIONNAIRE FOR CIVIL CASES

JUROR QUESTIONNAIRE Code of Civil Procedure Section 205(c)-(d) Sec. 1. Statutory Authority This Juror Questionnaire has been drafted under the authority of Code of Civil Procedure section 205(c)-(d) and

### Outline 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

### Introduction to the Practice of Statistics Fifth Edition Moore, McCabe

Introduction to the Practice of Statistics Fifth Edition Moore, McCabe Section 5.2 Homework Answers 5.29 An automatic grinding machine in an auto parts plant prepares axles with a target diameter µ = 40.125

### IDENTITY AND INTERNET SAFETY CURRICULUM

IDENTITY AND INTERNET SAFETY CURRICULUM INTRODUCTION Consider the following statistics: 96 percent of teens use social networking applications such as Facebook, MySpace, Chat rooms, and blogs 1 70 percent

### Describing Data and Descriptive Statistics

Describing Data and Descriptive Statistics Peter Moffett MD May 17, 2012 Introduction Data can be categorized into nominal, ordinal, or continuous data. This data then must summarized using a measure of

### What Does the Normal Distribution Sound Like?

What Does the Normal Distribution Sound Like? Ananda Jayawardhana Pittsburg State University ananda@pittstate.edu Published: June 2013 Overview of Lesson In this activity, students conduct an investigation

### Science: it s a people thing A discussion workshop for girls

CONTENTS Supporting Materials 1. Background notes for facilitators 2-3 2. Running your workshop: Options 1 and 2 4-8 3. Planning checklist 9 4. Role model guidelines 10-12 5. Further information 13 1.

### PowerTeaching i3: Algebra I Mathematics

PowerTeaching i3: Algebra I Mathematics Alignment to the Common Core State Standards for Mathematics Standards for Mathematical Practice and Standards for Mathematical Content for Algebra I Key Ideas and

### 6. Decide which method of data collection you would use to collect data for the study (observational study, experiment, simulation, or survey):

MATH 1040 REVIEW (EXAM I) Chapter 1 1. For the studies described, identify the population, sample, population parameters, and sample statistics: a) The Gallup Organization conducted a poll of 1003 Americans

### California Treasures High-Frequency Words Scope and Sequence K-3

California Treasures High-Frequency Words Scope and Sequence K-3 Words were selected using the following established frequency lists: (1) Dolch 220 (2) Fry 100 (3) American Heritage Top 150 Words in English

### Statistics 2014 Scoring Guidelines

AP Statistics 2014 Scoring Guidelines College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is the official online home

### HYPOTHESIS 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

### Money Math for Teens. Introduction to Earning Interest: Middle School Version

Money Math for Teens Introduction to Earning Interest: Middle School Version This Money Math for Teens lesson is part of a series created by Generation Money, a multimedia financial literacy initiative

### Notes 8: Hypothesis Testing

Notes 8: Hypothesis Testing Julio Garín Department of Economics Statistics for Economics Spring 2012 (Stats for Econ) Hypothesis Testing Spring 2012 1 / 44 Introduction Why we conduct surveys? We want

### Fundamentals of Probability

Fundamentals of Probability Introduction Probability is the likelihood that an event will occur under a set of given conditions. The probability of an event occurring has a value between 0 and 1. An impossible

### II. DISTRIBUTIONS distribution normal distribution. standard scores

Appendix D Basic Measurement And Statistics The following information was developed by Steven Rothke, PhD, Department of Psychology, Rehabilitation Institute of Chicago (RIC) and expanded by Mary F. Schmidt,

### Size of a study. Chapter 15

Size of a study 15.1 Introduction It is important to ensure at the design stage that the proposed number of subjects to be recruited into any study will be appropriate to answer the main objective(s) of

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

STATISTICS/GRACEY PRACTICE TEST/EXAM 2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Identify the given random variable as being discrete or continuous.

### Mean Feast. Teacher s Pages. Essentials. Concepts or Skills: Vocabulary: mean, average, median, NCTM Standard(s): Common Core Standards: Objectives:

10 Teacher s Pages Mean Feast Essentials Concepts or Skills: Measures of central tendency Vocabulary: mean, average, median, mode, range, outliers, data sets NCTM Standard(s): Data Analysis and Probability

### Introduction to Statistics for Psychology. Quantitative Methods for Human Sciences

Introduction to Statistics for Psychology and Quantitative Methods for Human Sciences Jonathan Marchini Course Information There is website devoted to the course at http://www.stats.ox.ac.uk/ marchini/phs.html

### **Chance behavior is in the short run but has a regular and predictable pattern in the long run. This is the basis for the idea of probability.

AP Statistics Chapter 5 Notes 5.1 Randomness, Probability,and Simulation In tennis, a coin toss is used to decide which player will serve first. Many other sports use this method because it seems like

### Chapter 6 ATE: Random Variables Alternate Examples and Activities

Probability Chapter 6 ATE: Random Variables Alternate Examples and Activities [Page 343] Alternate Example: NHL Goals In 2010, there were 1319 games played in the National Hockey League s regular season.

### Non-Parametric Tests (I)

Lecture 5: Non-Parametric Tests (I) KimHuat LIM lim@stats.ox.ac.uk http://www.stats.ox.ac.uk/~lim/teaching.html Slide 1 5.1 Outline (i) Overview of Distribution-Free Tests (ii) Median Test for Two Independent

### Teaching & Learning Plans. The Correlation Coefficient. Leaving Certificate Syllabus

Teaching & Learning Plans The Correlation Coefficient Leaving Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what the lesson, or series of lessons, hopes to

### Lesson 13: Games of Chance and Expected Value

Student Outcomes Students analyze simple games of chance. Students calculate expected payoff for simple games of chance. Students interpret expected payoff in context. esson Notes When students are presented

### What If? A Lesson Plan from Rights, Respect, Responsibility: A K-12 Curriculum

What If? A Lesson Plan from Rights, Respect, Responsibility: A K-12 Curriculum Fostering responsibility by respecting young people s rights to honest sexuality education. NSES ALIGNMENT: By the end of